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The CORRECT answer is (d) 0.096

The best I can explain: Given: The refractive INDEX for VIOLET color = 1.456; Refractive index for RED color = 1.414

Required equation ➔

ω=\(\frac {\mu_V – \mu_R}{\mu – 1}\)

Also, μ=\(\frac {(\mu_V+\mu_R)}{2}\)

μ=\(\frac {1.456+1.414}{2}\)=1.435

Thus, ω=\(\frac {1.456-1.414}{1.435-1}\)

ω=\(\frac {0.042}{0.435}\)

ω=0.096

Therefore, the dispersive power of crown glass is 0.096.

Right CHOICE is (b) FOUR times

For explanation I would say: On doubling the diameter, the area of the objective increases four times. Its light-gathering POWER increases four times. The brightness of the image also increases four times. THEREFORE, the INTENSITY of the image increases by four.

Right ANSWER is (b) False

Easy EXPLANATION: No, this is a false statement. The upper PART of the bi-focal lens should be a concave lens, whereas the one used for DISTANT vision as its lower part should be a convex lens. Such a bi-focal lens is used for reading PURPOSES.

Right option is (b) 2

For explanation I WOULD say: Generally, there are two kinds of rainbows, namely primary rainbow and secondary rainbow. The primary rainbow occurs due to one internal reflection and two REFRACTIONS, whereas secondary rainbow occurs due to two internal REFLECTIONS and two refractions, from the WATER drops suspended in the air.

Right OPTION is (a) Angle of deviation

Explanation: A PRISM is a homogenous, TRANSPARENT medium enclosed two plane surfaces inclined at an angle. These surfaces are called the refracting surfaces and the angle between the incident ray and EMERGENT ray is known as the angle of deviation.

Right option is (a) Reduces

Explanation: The fly will not be seen in the FINAL image. But the intensity of the final image GETS reduced because light will not enter the telescope from that PART of the object where the fly is SITTING. Therefore, a REDUCTION effect will be observed in the final image of the fly.

The correct option is (B) The rays have to travel a shorter distance than usual at sunrise and SUNSET

Explanation: During sunrise and sunset, the rays have to travel a large part of the atmosphere since the rays are CLOSE to the HORIZON at that time. That is why, red being the least scattered ENTERS our eyes, as all the other colors get scattered away.

Right answer is (b) Angular DISPERSION

To explain I would say: The DIFFERENCE in a deviation between any TWO colors is KNOWN as angular dispersion. Angular dispersion is given as:

δV-δR=(μV-μR)A

Where μV and μR are the refractive index for VIOLET rays and red rays, respectively. Mean deviation is δ = \( ( \frac {\delta_V + \delta_R}{2} ) \).

The correct OPTION is (a) 2

For explanation: Given: f = +10 CM; v = -30 cm

Required equations ➔

\(\frac {1}{f}=\frac {1}{v}-\frac {1}{U}\)

m=\(\frac {size \, of \, the \, image}{size \, of \, the \, object}=\frac {v}{u}\)

\(\frac {1}{u}=\frac {1}{v}-\frac {1}{f}=\frac {1}{-30}-\frac {1}{10} = \frac {-(10+30)}{300} = \frac {-40}{300}= \frac {-2}{15}\)

u=\(\frac {-15}{2}\) = -7.5 cm

m=\(\frac {v}{u}= – \frac {30}{-7.5}=\frac {-300}{-75}\)= +4

Therefore, the object should be placed at a distance of 7.5 cm from the lens to GET the image at a distance of 30 cm from the lens. It is four times enlarged and is erect.

Right ANSWER is (d) 71.5 cm

The best I can explain: Given: R1 = 50 cm; R2 = 20 cm; μ2 = 1.2

Required equation ➔ \(\frac {1}{f}\)=(μ-1)\( ( \frac {1}{R_1} – \frac {1}{R_2} ) \)

 \(\frac {1}{f}=( \frac {\mu 2}{\mu 1} -1 ) ( \frac {1}{R_1} – \frac {1}{R_2} ) \)

 \(\frac {1}{f}=( \frac {1.2}{1} -1 ) ( \frac {1}{50} – \frac {1}{-20} ) \)

 \(\frac {1}{f}\)=(0.2)\( ( \frac {1}{50} + \frac {1}{20} ) \)

 \(\frac {1}{f}\)=(0.2)\( ( \frac {20}{1000} + \frac {50}{1000} ) \)

 \(\frac {1}{f}\)=(0.2)\( ( \frac {7}{100} ) \)

\(\frac {1}{f}\)=0.014

f=+71.5 cm

Right answer is (c) Rainbow

The explanation: A rainbow is an example of a dispersion of sunlight by the WATER drops in the atmosphere. This is a phenomenon due to the combined EFFECT of dispersion, refraction, and reflection of sunlight by spherical water droplets of rain. OTHERS all are common ILLUSTRATIONS of scattering of LIGHT.

The correct CHOICE is (c) Myopia

For explanation I would say: As the focal length is negative, the lens used is CONCAVE. When a person is prescribed a concave lens, then the person is considered to be SUFFERING from MYOPIC. Therefore, the boy is suffering from myopia.

Right ANSWER is (C) 1^o

The best I can EXPLAIN: The required equation ➔ δ=(μ-1)A

When two prisms are combined, then:

δ=δ+δ’=(μ-1)A+(μ’-1)A’=0

So, A’=-\(\frac {(\mu-1)A}{\mu^{‘}-1}\)

A’=-\(\frac {(1.15-1)}{1.45-1}\) × 3

A’=-1^o

Therefore, the angle of the other prism is 1^o and OPPOSITE of the first prism.

Correct CHOICE is (b) – 7.1 cm

Explanation: Angular magnification is maximum when the FINAL image is formed at the near point.

\(\FRAC {1}{u} = \frac {1}{V} – \frac {1}{f}\)

\(\frac {1}{u} = ( \frac {-1}{25} ) – ( \frac {1}{10} ) \)

u = -7.1 cm.

Therefore, the OBJECT should be placed 7.1 cm before the lens to avoid angular magnification.

Correct choice is (b) BEES

To elaborate: Bees have some retinal CONES that are sensitive to ultra-violet light, so they can SEE objects in ultra-violet light. Humans are ultra-violet blind. Therefore, a human being cannot see UV light, whereas bees can.

The correct CHOICE is (d) 50 cm

Easiest EXPLANATION: In a telescope, the objective should have a LARGE focal length than the eyepiece. So the LENS of 50 cm focal length will be used as the objective. So, the SMALLER one of the two, i.e. the 5 cm focal length lens will be used as the eyepiece.

Right answer is (b) μ=A+\(\FRAC {B}{\lambda^2} + \frac {C}{\lambda^4}\)

For EXPLANATION I would say: CAUCHY’s dispersion formula is an empirical expression that gives an approximate relation between the refractive index of a medium and the WAVELENGTH of the light. Cauchy’s formula is given as:

μ=A+\(\frac {B}{\lambda^2} + \frac {C}{\lambda^4}\)

Where A, B, and C are the ARBITRARY constants of the medium.

The correct answer is (d) Dispersive power = \(\frac {angular \, dispersion}{MEAN \, deviation}\)

The explanation: The formula for dispersive power is given as:

Dispersive power (ω)=\(\frac {Angular \, dispersion (\delta_V-\delta_R)}{Mean \, deviation (\DELTA)}\)

ω=\(\frac {\mu_V-\mu_R}{\mu-1}\)

Where μ=\(\frac {\mu_V+\mu_R}{2}\) = mean REFRACTIVE INDEX

Right ANSWER is (c) Increasing the diameter of the objective

The explanation is: The light-gathering power of the objective will increase and even FAINT OBJECTS will BECOME visible. This is DONE by increasing the diameter of the objective. So, by increasing the diameter of the objective, the range of the telescope can be increased.

The correct choice is (a) True

The best explanation: Yes, the secondary rainbow is fainter than the PRIMARY rainbow. As the secondary rainbow is formed by ONE more reflection than the primary rainbow, it is much fainter than the primary rainbow. The colors are also reversed in the secondary rainbow. In the primary rainbow, the violet COLOR is on the INNER EDGE and red color is on the outer edge. It is the other way round for the secondary rainbow.

Correct answer is (a) Rayleigh SCATTERING

Easy explanation: Light of shorter WAVELENGTHS is scattered much more than light of LONGER wavelengths. The amount of scattering is inversely PROPORTIONAL to the fourth power of the WAVELENGTH. This is known as Rayleigh scattering.

Correct option is (c) 1 D

The explanation is: Pw=\(\FRAC {\mu_w}{f_w}\)=μw\( [ \frac {\mu_g}{\mu_w} -1 ] [ \frac {1}{R1} – \frac {1}{R2} ]\)……………………………..1

Pa=\(\frac {1}{f_a}\)=[μg-1]\([ \frac {1}{R1} – \frac {1}{R2} ]\)……………………………………2

Dividing 1 and 2

We GET ➔ \(\frac {P_w}{P_a} = \frac {\mu_g-\mu_w}{μ_g-1}\)

Pw=\(\frac {\frac {3}{2}-\frac {4}{3}}{\frac {3}{2}-1}\) × 3

Pw=\(\frac {\frac {1}{6}}{\frac {1}{2}}\) × 3

Pw=\(\frac {2\times 3}{6}\)=1 D

Therefore, the power of the lens gets altered inside water.

Right choice is (C) + 50 CM

Best explanation: By thin LENS formula,

\(\frac {1}{f} = \frac {1}{v} – \frac {1}{U}\)

\(\frac {1}{f} = \frac {1}{(-50)} – \frac {1}{(-25)}\)

f = +50 cm.

Correct choice is (c) 13 cm

The BEST I can explain: Given: f = + 20 cm; v = + 40 cm

The required equation ➔

\(\FRAC {1}{f}=\frac {1}{v}-\frac {1}{U}\)

\(\frac {1}{10}=\frac {1}{10}-\frac {1}{u}\)

\(\frac {1}{u}=\frac {1}{10}-\frac {1}{40} = \frac {40-10}{400}\)

\(\frac {1}{u}=\frac {30}{400}=\frac {3}{40}\)

u=\(\frac {40}{3}\)=13.3 cm

Right answer is (a) True

Explanation: Yes, this statement is true. The REFRACTIVE index is the property of a material. Since δ=(μ-1)A, different colors turn through different ANGLES on PASSING through the prism. This is the cause of dispersion. THEREFORE, the refractive index of a material of a prism is different for different colors.

The correct answer is (a) Independent

Best explanation: MAGNIFYING power of a TELESCOPE is given as:

m = \(\frac {f_0}{f_e}\)

It is independent of the APERTURE of the OBJECT. So the magnifying power is not affected when the diameter of the OBJECTIVE is increased.

Right choice is (c) The ANGLE of reflection

For explanation: Factors on which the angle of deviation DEPENDS are ➔ the angle of incidence, the MATERIAL of the prism, the wavelength of light used, and the angle of the prism. So, the FACTOR on which the angle of deviation that does not depend on is the angle of reflection.

Right choice is (b) False

The EXPLANATION is: Light suffers two total INTERNAL reflections in the FORMATION of the secondary rainbow. So more light intensity is ABSORBED. Therefore, the secondary rainbow will be fainter compared to the primary rainbow and the latter will be brighter.

Right CHOICE is (d) Yes

To EXPLAIN: Yes. The refractive index of a medium concerning another medium can be less than UNITY. For example, the relative refractive index of WATER concerning glass is less than unity.

Correct answer is (B) False

To explain: No, this is a false statement. The power of a convex lens is POSITIVE as a convex lens has a positive FOCAL length, while the power of a CONCAVE lens is negative as a concave lens has a negative focal length.

Right option is (c) LESS than UNITY

The EXPLANATION: Absolute refractive index = \( \frac {Speed \, of \, LIGHT \, in \, vacuum}{Speed \, of \, light \, in \, the \, medium}\). The relative refractive index of water with respect to GLASS is less than unity.

The CORRECT option is (a) True

For explanation: Yes, this is a true statement. SIGN CONVENTIONS for spherical refracting surface are the same as those for spherical mirrors. The only difference is that instead of the pole of the mirror, we USE the optical CENTER of a lens.

The correct choice is (c) BLUE

The best I can explain: The Ocean is blue because water absorbs colors in the red PART of the LIGHT spectrum. LIKE a filter, this leaves behind colors in the blue part of the light spectrum for us to see. So, the blue color of the ocean is due to the preferential scattering of light by water molecules.

Correct ANSWER is (c) Reflection of light

The best I can explain: When the sun or the MOON is seen through a thin veil of high clouds, haloes, i.e. rings, are seen. These are formed due to the reflection of light by the icy CRYSTALS present in the atmosphere. So, this is the cause of rings AROUND the sun or the moon.

The correct choice is (b) False

For explanation I would say: No, this STATEMENT is false. APPARENT DEPTH is maximum for that part of the bottom of the tank which is observed NORMALLY. Apparent depth decreases with increasing OBLIQUITY. Therefore, the refraction in a water tank does not make apparent depth the same throughout.

Right option is (a) 2

To explain I WOULD say: The portion of a refracting medium, whose CURVED surface forms the part of a sphere, is known as a SPHERICAL refracting surface. Spherical refracting SURFACES are of TWO types, namely, convex refracting spherical surface and concave refracting spherical surface.

The correct answer is (d) f is negative for CONCAVE lens

Explanation: Thin lens formula is given as:

\(\FRAC {1}{f}=\frac {1}{V}-\frac {1}{u}\)

Where u = distance of the object from the optical center of the lens; v = distance of the IMAGE from the optical center of the lens; f = FOCAL length of a lens. According to the thin lens formula, f is positive for converging or convex lens and f is negative for a diverging or concave lens.

Right answer is (b) Scattering of light by WATER molecules

Explanation: The blue COLOR of the ocean is due to the preferential scattering of light by water molecules. This is the underlying reason for many other PHENOMENA such as why the sky is blue or the sky is reddish at the TIME of SUNRISE or sunset.

The correct choice is (a) REFRACTION

Explanation: The reason is that for a given angle f incidence, the reflection is the same for all the WAVELENGTHS of white light while the angle of refraction is different for different wavelengths. Therefore, this is how DISPERSION is CAUSED.

The CORRECT OPTION is (b) Concave mirror

For EXPLANATION: If the magnification of the mirror is one, then it is a PLANE mirror. If magnification is more than one, the mirror is concave. If magnification is less than one, then the mirror is convex. So the X required in this question is a concave mirror.

Correct answer is (c) DIOPTER

To elaborate: The power of a lens is defined as the reciprocal of its FOCAL length in meters. The expression is given as:

P = \(\FRAC {1}{f}\)

Where P is the power and f is the focal length in meters. Lens SURFACE power can be found with the index of refraction and the radius of CURVATURE. The SI unit of power of a lens is diopter.

The correct ANSWER is (c) 8.9 cm

To explain: \(\FRAC {1}{f}\) = (μ-1)\( [ \frac {1}{R_1} – \frac {1}{R_2} ] \)

\(\frac {1}{f}\) = (1.75 – 1)\( [ \frac {1}{10} – \frac {1}{(-20)} ] \)

\(\frac {1}{f} = \frac {9}{80}\)

f = +8.89 cm ≈ 8.9 cm.

Correct choice is (B) False

To explain I WOULD say: When light passes from a rarer to a DENSER medium, the wavelength of light changes but the frequency remains unchanged. Therefore, both frequency and wavelength do not CHANGE when light passes from a rarer to a denser medium.

Correct ANSWER is (a) The angle of incidence in the denser medium must be greater than the critical angle for the TWO media

The best I can explain: The necessary conditions for total internal REFLECTION are ➔ the light must TRAVEL from an OPTICALLY denser to an optically rarer medium and the angle of incidence in the denser medium must be greater than the critical angle for the two media.