Explore topic-wise InterviewSolutions in .

Given θ = 60°, 

Intensity of light incident on the polaroid = I_o, 

Intensity of light transmitted through the polaroid I = ? 

I = I₀ cos² θ => I = I₀ cos² 60° = I₀/4. 

Thus 25% of the light intensity is transmitted through the polaroids. 

Polaroids are the devices used to produce plane polarised light. 

Uses of polaroids: 

(1) To control the intensity of light in sunglasses, windowpanes, etc.. 

(2) In photographic cameras and 3D movie cameras.  

The required ratio is \(\cfrac{I_1}{I_2}\) = \(\cfrac{w_1}{w_2}\) = \(\cfrac23\)

Differences between interference of light and diffraction of light: 

Interference and diffraction are consistent with the principle of conservation of energy. 

(i) Any one of the values displayed by Puja curiosity/observation etc.

Any one of the values displayed by father concern / knowledge / sense of duty etc

(ii) Interference.of sunlight due to the soap bubble.

The intensity of light at that point will be close to the maximum intensity and the point will be nearly bright as the path difference = 2.999 λ ≈ 3λ (integral multiple of λ).

The required phase difference is (2m – 1)π rad 

= (2 × 11 – 1)π rad 

= 21π rad.

(C) 11 \(\cfrac λ 2\)

Interference and diffraction are consistent with the principle of conservation of energy. 

Class 12 Physics MCQ Questions of Wave Optics with Answers available free on the Sarthaks eConnect website. We have provided MCQ Questions for Class 12 Physics with Answers to help students understand the concept very well. Check the below Class 12 Physics MCQ Questions of Wave Optics with Answers. The Class 12 MCQ Questions are prepared after analyzing the syllabus prescribed by the NCERT and the previous year’s question papers.

Class 12 important MCQ Questions are prepared for the students preparing for the competitive exams like IIT-JEE, NEET, not only for the entrance exams this material will also help to score well in the CBSE board exam. Start practice The Wave Optics Class 12 Physics Multiple choice Questions with detailed explations it’s been prepared by the experts and the master teachers.

Practice MCQ Question for Class 12 Physics chapter-wise

1. Resolving power of telescope can be increased by increasing

(a) the wavelength
(b) the diameter of objective
(c) the diameter of eyepiece
(d) the focal length of eyepiece

2.  Polarisation of light proves

(a) corpuscular nature of light
(b) quantum nature of light
(c) transverse wave nature of light
(d) longitudinal wave nature of light

3. The wavefront due to a source situated at infinity is

(a) spherical
(b) cylindrical
(c) planar
(d) circular

4. A laser beam is coherent because it contains

(a) waves of several wavelengths
(b) incoherent waves of a single wavelength
(c) coherent waves of several wavelengths
(d) coherent waves of a single wavelength

5. When exposed to sunlight, thin films of oil on water of ten exhibit brilliant colours due to the phenomenon of

(a) interference
(b) diffraction
(c) dispersion
(d) polarisation

6. When compact disk is illuminated by a source of white light, coloured lines are observed. This is due to

(a) dispersion
(b) diffraction
(c) interference
(d) refraction

7. When unpolarised light beam is incident from air onto glass (n = 1.5) at the polarising angle.

(a) Reflected beam is polarised completely
(b) Reflected and refracted beams are partially polarised
(c) Refracted beam is plane polarised
(d) Whole beam of light is refracted

8. The phenomenon of interference is based on

(a) conservation of momentum
(b) conservation of energy
(c) conservation of momentum and energy
(d) quantum nature of light

9. In Young’s double slit experiment, if the monochromatic source of yellow light is replaced by red light, the fringe width

(a) increases
(b) decreases
(c) remains unchanged
(d) the fringes disappear

10. The idea of secondary wavelets for the. propagation of a wave was first given by

(a) Newton
(b) Huygens
(c) Maxwell
(d) Fresnel

11. Light propagates rectilinearly, due to

(a) wave nature
(b) wavelengths
(c) velocity
(d) frequency

12. The refractive index of glass is 1.5 for light waves of X = 6000 A in vacuum. Its wavelength in glass is

(a) 2000 Å
(b) 4000 Å
(c) 1000 Å
(d) 3000 Å

13. The phenomena which is not explained by Huygen’s construction of wavefront

(a) reflection
(b) diffraction
(c) refraction
(d) origin of spectra

14. When interference of light takes place

(a) energy is created in the region of maximum intensity
(b) energy is destroyed in the region of maximum intensity
(c) conservation of energy holds good and energy is redistributed
(d) conservation of energy does not hold good

15. To observe diffraction, the size of the obstacle

(a) should beX/2, where X is the wavelength
(b) should be of the order of wavelength
(c) has no relation to wavelength
(d) should be much larger than the wavelength

16. A single slit diffraction pattern is obtained using a beam of red light What happened the red light is replaced by the blue light?

(a) There is no change in diffraction pattern
(b) Diffraction fringes become narrower and crowded
(d) Diffraction fringes become broader and farther apart
(d) The diffraction pattern disappear

17. When a polaroid is rotated, the intensity of light varies but never reduces to zero. It shows that the incident light is:

(a) unpolarised
(b) completely plane polarised
(c) partially plane polarised
(d) None of the above

18. Two sources of light are said to be coherent when both give out light waves of the same:

(a) amplitude and phase
(b) intensity and wavelength
(c) speed
(d) wavelength and a constant phase difference

19. The theory of expanding universe is confirmed by the observation of the spectral lines of the star, which shows :

(a) green shift
(b) red shift
(c) violet shift
(d) yellow shift

20. Polaroid glasses is used in sun glasses because :

(a) It reduces the light intensity to half on account of polarization
(b) It is fashionable
(c) It has good colour
(d) It is cheaper

21. In Young’s double slit experiment, the central point on the screen is:

(a) bright
(b) dark
(c) first bright and later dark
(d) first dark and later bright

22. A person cannot see object clearly beyond 50 cm. The power of the lens to correct his vision is :

(a) +0.5 dioptre
(b) -0.5 dioptre
(c) -2 dioptre
(d) +2 dioptre

23. A young’s double slit experiment uses a monochromatic source. The shape of interference fringes formed on a screen is :

(a) parabola
(b) straight line
(c) circle
(d) hyperbola

24. Intensity of light depends on

(a) amplitude 
(b) frequency
(c) wavelength 
(d) velocity

25. Instead of using two slits, if we use two separate identical sodium lamps in Young’s experiment, which of the following will occur?

(a) General illumination
(b) Widely separate interference
(c) Very bright maxima
(d) Very dark minima

Answer :

1. Answer : (b) the diameter of objective

Explanation: As the wavelength of the incident light is fixed, we can increase the resolving power by increasing the diameter of the objective lens. Hence, in order to increase the resolving power, the diameter of the objective lens can be increased.

2. Answer : (c) transverse wave nature of light

Explanation: Polarisation explain the wave nature of light, as light wave are polarised in a particular plane. The longitudinal waves cannot to be polarised. So, transverse wave can only be polarised. Hence, polarisation of light proves the transverse nature of light.

3. Answer : (c) planar

Explanation: When you considered it a large distance and measuring justice Mall section of it then it can be considered to be plane wavefront source at Infinity example the one coming from sun to earth surface is considered to be plain VU friend from light diverging from a point source will be spherical So, the wave front due to a source situated at infinity is planar.

4. Answer : (d) coherent waves of a single wavelength

Explanation: LASER is the short form of Light Amplification by Stimulated Emission of Radiation. Laser beam is intense, monochromatic (that is of the single wavelength) collimated and highly coherent.

5. Answer : (a) interference

Explanation: The colour in the oil film is formed due to Interference of sunlight where the colour of the film will depend upon the thickness and the angle of inclination.

6. Answer : (b) diffraction

Explanation: The fine rulings, each 0,.5μm wide, on a compact disc function as a diffraction grating. When a small source of white light illuminates a disc, the light is diffracted from the rulings.

7. Answer : (b) Reflected and refracted beams are partially polarised

Explanation: If unpolarised light is incident at polarising angle, then reflected light is completely, i.e, 100% polarised.

8. Answer : (b) conservation of energy

Explanation: The phenomenon of interference is based on conservation of energy. The energy is distributed in the interference phenomena in such a way that the strength of the resultant wave is maximal at certain spots and minimum at others, the phenomenon of interference is based on energy conservation.

9. Answer : (a) increases

Explanation: Using the relation for fringe width β = Dλ/2d hence, β∝λ Since, λ_red >λ_yellow.  Therefore using the red light in place of yellow light, fringe width will increase.

10. Answer : (b) Huygens

Explanation: Huygens principle states that every point on a wavefront is a source of secondary wavelets. These wavelets spread out in the forward direction, at the same speed as the source wave. The new wavefront is a line tangent to all of the wavelets.

11. Answer : (a) wave nature

Explanation: Light propagates rectilinearly. But it can take a slight turn at obstacles. This property of light is due to its wave nature.

12. Answer : (b) 4000 Å

Explanation: 

\(\mu=\frac{c}{v}=\frac{\lambda_v}{\lambda_g}\)

\(\therefore\lambda_g=\frac{\lambda_u}{\mu}\)

\(=\frac{6000}{1.5}\)

= 4000 Å

13. Answer : (d) origin of spectra

Explanation: The Huygen's construction of wavefront does not explain the phenomena of origin of spectra.

14. Answer : (c) conservation of energy holds good and energy is redistributed

Explanation: Interference is a phenomenon in which two waves superimpose to form a resultant wave of greater of lower amplitude. There is no loss of energy during interference. It is simply redistributed.

15. Answer : (b) should be of the order of wavelength

Explanation: To observed diffraction, the size of the obstacle should be of the order of wavelength. i.e. λ = d.

16. Answer : (b) Diffraction fringes become narrower and crowded

Explanation: As λ_blue < λ_red, and width of diffraction bands is directly proportional to λ, therefore diffraction bands become narrower and crowded.

17. Answer : (c) partially plane polarised

Explanation: Polaroid cuts off plane polarised light for one orientation.

18. Answer : (d) wavelength and a constant phase difference

Explanation: As these sources are from a single original source, their frequency or wavelength will be the same. Thus, two sources of light are said to be coherent, when they give light waves of same wavelength and constant phase difference.

19. Answer : (b) red shift

Explanation: bservations show that the spectral lines of distant galaxies are redshifted, and that their recession velocities are proportional to their distances from us, a relationship known as Hubble's law.

20. Answer : (a) It reduces the light intensity to half on account of polarization

Explanation: When light is reflected from flat surfaces becomes polarised, meaning travels in a uniform direction. To overcome this, polarised lenses are used.

21. Answer : (a) bright

Explanation: In the normal adjustment of YDSE, Path difference between the waves at central location is always zero. So maxima is obtained at central position. Central point on the screen is bright.

22. Answer : (c) -2 dioptre

Explanation: Here v = - 50 mm, u = ∞

Hence using 1/f =1/v=1/u we find f = - 50 cm = 0.50 m

So power of the lens is P = 1/ −0.50m =−2D

23. Answer : (b) straight line

Explanation: Monochromatic means light with single wavelength .Hence shape of interference fringes formed on the screen is straight line. If instead of double slit experiment double hole experiment was given shape would have been hyperbolla.

24. Answer :(a) amplitude 

Explanation: Light is an electromagnetic wave. its intensity will depend on the amplitude of the wave. The amplitude of light is measured in volts per meter in one direction perpendicular to its propagation direction.

25. Answer : (a) General illumination

Explanation: The superimposing waves will not be in constant phase. This leads to general illumination.

Click here to practice  MCQ Question for Wave Optics Class 12

In 1865, James Clerk Maxwell developed a mathematical theory on the intimate relationship between electricity and magnetism. His theory predicted light to be a high-frequency transverse electromagnetic wave in ether. Electric and magnetic fields in the wave vary periodically in space and time at right angles to each other and to the direction of propagation of the wave.

The speed of the electromagnetic waves in a medium, as calculated on the basis of Maxwell’s theory, was experimentally found to be equal to the measured speed of light in that medium. Maxwell’s electromagnetic theory of light, with addition by others till 1896, could account for all the known phenomena regarding the propagation (or transmission) of light through space and through matter.

Like other chapters wave optics will help you to score good marks in the board exams of class 12. Include our Wave Optics Class 12 Mock Test Series in your preparations and score well in your exams. Practicing Wave Optics Online Mock Test for Class 12  is one of the best ways to prepare for the CBSE Class 12 board exam. There is no substitute for consistent practice whether one wants to understand a concept thoroughly or one wants to score better. 

The study of various phenomena such as polarization, diffraction, interference and other occurrences where ray approximation of geometric optics cannot be done. Thus, the section of optics that deals with the behavior of light and its wave characteristics is said to be wave optics.

Students can solve these Wave Optics Class 12  Online Mock Test and assess their preparation level. Mock Test Solving the Wave Optics Multiple Choice Questions of Class 12 Physics Chapter 10 Mock Test can be of extreme help as you will be aware of all the concepts.

Click here to start practice: - Class 12 Wave Optics Mock Test

It is not possible to explain certain phenomena of light, such as interference, diffraction and polarization, with the help of ray optics (geometrical optics). The branch of optics which uses wave nature of light to explain these optical phenomena is called wave optics.

The phenomena of spreading of light from narrow holes or slits when the edges of holes/slits are of the order of wavelength of light is called diffraction.  

1. A Polaroid lens filter makes use of polarization by reflection. This filter is used in photography to reduce or eliminate glare from reflective nonmetallic surfaces like glass, rock faces, water and foliage. It can also deepen the colour of the skies.

2. Polaroid sunglasses reduce the transmitted intensity by a factor of one half and also reduce or eliminate glare from nonmetallic surfaces such as asphalt roadways and snow fields.

3. Polaroid filters are used in liquid crystal display (LCD) screens. 

4. Polaroids are used to produce and show 3-D movies to give the viewer a perception of depth.

[Note :Three-dimensional movies are filmed from two slightly different camera locations and shown at the same time through two projectors fitted with polarizers having different transmission axes. The audience wear glasses which have two Polaroid filters whose transmission axes are the same as those on the projectors.]

(a) be a fine sharp slit white in colour at the center.

(c) The intensity of light as seen through the Polaroid shall go through a minimum but not zero for two orientations of the polaroid. 

No, because the phase difference between light coming from two independent sources continuously change. 

The point will be nearly dark as the path difference = 7.4999 λ 

≈ (8 – 0.5) λ, which is of the form

(m – \(\cfrac12\))λ, where m = 1, 2, … …. 8

When a narrow slit is placed in front of an intense source of monochromatic light, cylindrical wave-fronts propagate from the slit. In Young’s experiment, two coherent sources are then obtained by wavefront splitting by placing a second screen with two narrow slits at a small distance from the first slit.

(a) Wave normal: A wave normal at a point on a wave front is defined as a line drawn perpendicular to the wave front in the direction of propagation of the wave front.

In a homogeneous isotropic medium, a wave front moves parallel to itself. Thus, at any point in the medium, the direction in which the wave front moves is always perpendicular to the wave front at that point. This direction is given by the wave normal at that point.

(b) Ray of light: The direction in which light is propagated is called a ray of light.

This term (ray of light) is also used to mean a narrow beam of light waves. Only in a homogeneous isotropic medium is a ray of light the same as a wave normal. For spherical wave fronts spreading out from a point source, the rays are radially divergent. The rays corresponding to a plane’ wave front form a parallel beam.

1. The electromagnetic waves are transverse in nature as they propagate by oscillating electric and magnetic fields that are perpendicular to each other and also perpendicular to the direction of propagation of the wave. 

2. These waves do not require any material medium for their propagation, i.e., they can travel even through vacuum. 

3. The wavelength of the electromagnetic waves ranges from very small (< 1 fm) to very large (> 1 km). The waves are classified in the order of increasing wavelength as γ-rays, X rays, ultraviolet, visible, infrared, microwave and radio waves.

4. In vacuum, the speed of electromagnetic waves does not depend on the frequency of the wave. But, in a material medium, it depends on the frequency. For a given frequency, the speed is different in different mediums. 

[Note : 1 fm (femtometre) = 10^-15 m]

A ray of light is the path along which light energy is transmitted from one point to another in an optical system.

To explain the interaction of light and matter (as in the emission or absorption of radiation), Max Planck, in 1900, and Einstein, in 1905, hypothesized light as concentrated or localized packets of energy. Such an energy packet is called a quantum of energy, which was given the name photon much later, in 1926, by Frithiof Wolfers and Gilbert Newton Lewis. For a radiation of frequency v, a quantum of energy is hv, where h is a universal constant, now called Planck’s constant.

[Note : ‘Localisation’ of energy in a region gives light its particle nature while frequency is a wave characteristic. The complementary properties of particle and wave of light quanta are reconciled as follows : light propagates as wave but interacts with matter as particle.]

The absolute refractive index of a medium is defined as the ratio of the speed of light in vacuum to the speed of light in the medium.

[Note : Absolute refractive index of a medium (n) 

= \(\cfrac{speed\,of\,light\,in\,vacuum\,(c)}{speed\,of\,light\,in\,the\,medium\,(v)}\)

The absolute refractive index of vacuum is 1 (by definition) and that of air is greater than 1, but very nearly equal to 1.]

Data : λ = 5600 A = 5.6 × 10^-7 m

Order of the dark fringe is 8,

∴ m = 8

For the fringe to be dark, path difference

= (2m – 1) \(\cfrac λ2\)

∴ Path difference, ∆l = (2 × 8 – 1) \(\cfrac λ2\) = 7.5λ

= 7.5 × 5.6 × 10^-7 m

= 4.2 × 10^-6 m

Phase difference, φ = \(\cfrac{2\pi}λ\) x ∆l

= \(\cfrac{2\pi}{5.6\times10^{-7}}\) × 4.2 × 10^-6 = 15π

(A) directly proportional to the wavelength

Huygens’ wave theory of light [Christiaan Huygens (1629-95), Dutch physicist] :

1. Light emitted by a source propagates in the form of waves. Huygens’ original theory assumed them to be longitudinal waves. 

2. In a homogeneous isotropic medium, light from a point source spreads by spherical waves. 

3. It was presumed that a wave motion needed a medium for its propagation. Hence, the theory postulated a medium called luminiferous ether that exists everywhere, in vacuum as well as in transparent bodies. Ether had to be assigned some extraordinary properties, a high modulus of elasticity (to account for the high speed of light), zero density (so that it offers no resistance to planetary motion) and perfect transparency.

4. The different colours of light are due to different wavelengths.

Merits :

1. Huygens’ wave theory satisfactorily explains reflection and refraction as well as their simultaneity. 

2. In explaining refraction, the theory concludes that the speed of light in a denser medium is less than that in a rarer medium, in agreement with experimental findings. 

3. The theory was later used by Young in 1800-04, Fraunhofer and Fresnel in 1814 to satisfactorily explain interference, diffraction and rectilinear propagation of light. The phenomenon of polarization could also be explained considering the light waves to be transverse.

Demerits :

1. It was found much later that the hypothetical medium, luminiferous ether, has no experimental basis. Einstein discarded the idea of ether completely in 1905. 

2. Phenomena like absorption and emission of light, photoelectric effect and Compton effect, cannot be explained on the basis of the wave theory.

[Note: To decide between the particle and wave theories of light, Dominique Francois Jean Arago (1786-1853), French physicist, suggested the measurement of the speed of light in air and water. The experiment was performed in 1850 by Leon Foucault (1819- 68), French physicist, using Arago’s experimental equipment. He found that the speed of light in water is less than that in air.]

dⁿw = \(\cfrac{v_a}{v_w}\) = \(\cfrac{vλ_a}{vλ_w}\) 

= \(\frac43\) gives \(\lambda_w\) = \(\frac34\lambda_a\)

= 0.75 \(\lambda_a\)

as the wavelength of the light in water.

The wavelength and speed of light change, but the frequency remains the same.

When a source of unpolarized light is viewed through a polarizer, the intensity of the light transmitted by the polarizer is reduced and hence the source appears less bright.

Correct option is: (D) frequency

Correct option is: (B) decreases

Coherent sources : Two sources of light are said to be coherent if the phase difference between the emitted waves remains constant. It is not possible to observe interference pattern with light from any two different sources. This is because, no observable interference phenomenon occurs by superposing light from two different sources. This happens due to the fact that different sources emit waves of different frequencies. Even if the two sources emit light of the same frequency, the phase difference between the wave trains from them fluctuates randomly and rapidly, i.e., they are not coherent.

Consequently, the interference pattern will change randomly and rapidly, and steady interference pattern would not be observed.

The answer is (A) interference

Brewster’s angle/Polarising angle(i_B): The angle of incidence for which the reflected light is completely plane polarised is called Brewster’s angle. 

Data : n_g = 1.46, c = 3 × 10⁸ m/s c

n_g = \(\cfrac{c}v\)

v = \(\cfrac{c}n\) = \(\cfrac{3\times10^8}{1.46}\) = 2.055 × 10⁸ m/s 

This is the speed of light in glycerine.

In unpolarised wave the displacement will be randomly changing with time though it will always be perpendicular to the direction of propagation. Natural light, e.g., from the sun is unpolarised. This means the electric vector takes all possible directions in the transverse plane, rapidly and randomly, during a measurement. A polaroid transmits only one component (parallel to a special axis). The resulting light is called linearly polarised or plane polarised. 

Thomas Young.

The modification in the distribution of light energy due to the superposition of two or more waves of light is called interference of light. 

Maximum intensity of light in Young’s double slit experiment is 4I_o. 

The conditions necessary for obtaining well defined and steady interference pattern :

1. The two sources of light should be coherent: The two sources must maintain their phase relation during the time required for observation. If the phases and phase difference vary with time, the positions of maxima and minima will also change with time and consequently the interference pattern will change randomly and rapidly, and steady interference pattern would not be observed. For coherence, the two secondary sources must be derived from a single original source.

2. The light should be monochromatic : Otherwise, interference will result in complex coloured bands (fringes) because the separation of successive bright bands (fringes) is different for different colours. It also may produce overlapping bands.

3. The two light sources should be of equal brightness, i.e., the waves must have the same amplitude. The interfering light waves should have the same amplitude. Then, the points where the waves meet in opposite phase will be completely dark (zero intensity). This will increase the contrast of the interference pattern and make it more distinct. 

4. The two light sources should be narrow : If the source apertures are wide in comparison with the light wavelength, each source will be equivalent to multiple narrow sources and the superimposed pattern will consist of bright and less bright fringes. That is, the interference pattern will not be well defined.

5. The interfering light waves should be in the same state of polarization : Otherwise, the points where the waves meet in opposite phase will not be completely dark and the interference pattern will not be distinct.

6. The two light sources should be closely spaced and the distance between the screen and the sources should be large : Both these conditions are desirable for appreciable fringe separation. The separation of successive bright or dark fringes is inversely proportional to the closeness of the slits and directly proportional to the screen distance.

(b) 90°

Explanation: Angle between the plane of vibration and plane of polarization is 90°.

(a) The scattering of light

Explanation: The reddish appearance of the sun at sunrise and sunset is due to the scattering of light.

Data : d₁ = 4.5 mm = 4.5 × 10^-3 m,

λ = 4500 Å = 4.5 × 10^-7 m,

distance between the slit and the eyepiec = distance between the slit and the biprism + distance between the biprism and the eyepiece 

= 10 cm + 80 cm = 90 cm = 0.9 m, 

u₁ = 30 cm = 0.3 m 

v₁ = D – u₁ 

= 0.9 m – 0.3 m 

= 0.6 m

Linear magnification of a lens,

\(\cfrac{image\,size}{object\,size}\) = \(\cfrac{image\,distance}{object\,distance}\)

\(\therefore\) \(\cfrac{d_1}d\) = \(\cfrac{v_1}{u_1}\)

\(\therefore\) d = \(\cfrac{d_1u_1}{v_1}\) = \(\cfrac{4.5\times10^{-3}\times0.3}{0.6}\)

\(\therefore\) d = 2.25 x 10^-3 m

\(\therefore\) The fringe width,

W = \(\cfrac{\lambda D}d\) = \(\cfrac{4.5\times10^{-7}\times0.9}{2.5\times10^{-3}}\) = 2 x 0.9 x 10^-4

= 1.8 x 10^-4 m

= 0.18 mm

Data : λ = 5100 Å = 5.1 × 10^-7 m,

W = \(\cfrac 2{10}\) cm = 2 × 10^-3 m,

D = 200 cm = 2 m

W = \(\cfrac{λD}d\)

∴ d = \(\cfrac{λD}W\) = \(\cfrac{5.1\times10^{-7}\times2}{2\times10^{-3}}\)

= 5.1 × 10^-4 m 

This is the slit-separation.

The distance between two consecutive bright (or two consecutive dark) fringes is called fringe width.

Interference pattern disappears. 

Data : n = \(\frac43\), 

i = 90\(^\circ\) - 40\(^\circ\) = 50\(^\circ\)

n = \(\cfrac{sin\,i}{sin\,r}\)

\(\therefore\) sin r = \(\cfrac{sin\,i}{n}\) = \(\cfrac{sin\,50^\circ}{4/3}\)

= \(\cfrac{0.7660}{4/3}\)

∴ The angle of refraction, r = sin^-1 (0.5745) = 35°4′