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(b) consecutive fringes will come closer

EXPLANATION:   

The options (a), (c) and (d) are related to the intensity changes. Since the intensity of light incident on the slits is not changed hence there will be no change in the intensity of the fringes. These options are not true.           

The fringe width is given as w = Dλ/d.  In this experiment D and d are not changed only λ is changed. Since the violet has smaller λ than the red light, so the fringe width will decrease. Hence the consecutive fringes will come closer. Option (b) is true.

(c) v_A = v_B = v_c.

(d) v_B =1/2 (v_A+v_c).

(b) have zero average value

(c) are perpendicular to the direction of propagation of light.

(d) are mutually perpendicular.

EXPLANATION:   

The electric and magnetic fields vary with time and position, hence (a) is not true.          Like in sinewave where the average value of displacement within a wavelength is zero, the average value of electric and magnetic fields are zero in the light waves. (b) is true.       

The direction of electric and magnetic fields are perpendicular to the direction of propagation of light. Option (c) is true.         

The electric and the magnetic fields are also mutually perpendicular to each other. i.e. if light travels in x-direction then electric and magnetic fields will be either in y and z-direction or in z and y directions. Option (d) is true.

The correct answer is (a) x = c.

EXPLANATION:  

 The wavefronts are perpendicular to the direction of the light. Since here the light is traveling along X-axis, the wavefront will be a plane perpendicular to the X-axis. Out of the four options only (a) represents a plane perpendicular to X-axis.

(c) find the new position of a wavefront

(d) explain Snell's law.

EXPLANATION:   

The Huygen's principle of secondary wavelets says that the points of a wavefront act as secondary sources of light emitting secondary wavelets. The line joining the points on the secondary wavelets that are in the same phase gives the new position of a wavefront. Hence the option (c) is true.         

It can also be used to explain the Snell's law. Hence the option (d) is true.   Options (a) and (b) are not true.

The correct answer is

(a) plane

Explanation:

When the point source or linear source of light is at very large distance, a small portion of spherical or cylindrical wavefront appears to be plane. Such a wavefront is plane wavefront. 

Interference occurs only with coherent sources which have an initial phase difference that does not change with time and have the same frequency. Two candles are not coherent sources hence we do not have an interference pattern.        

When the candles are replaced by laser sources they can produce interference pattern provided that they fulfil the conditions of coherent sources.

No, it is not necessary to have two waves of equal intensity to study interference pattern. But with the waves of unequal intensity, the clarity of the interference pattern will be affected. Because the resultant field E at a point is given as 

E² = E'² + E"² + 2E' E" cosẟ.  

E will not be zero for any value of ẟ. The destructive (dark) interference will not be completely dark and the contrast will be low.

(a) the fringe width will decrease

EXPLANATION:   

As the wavelength of light in water will decrease, hence the fringe width will decrease because the fringe width is proportional to the wavelength.

(c) remain same

EXPLANATION:   

The fringe width is given as w = Dλ/d where D = distance of the screen from the slits d = distance of slits. 

The wavelength λ remains the same when the light comes out of the film. Thus none of the entity D, d or λ changes. So the fringe with will remain the same. Hence the option (c).

Roughly the range of wavelengths from 620 nm to 780 nm is seen as red to human eyes. So the color of 620 nm and 780 nm can be broadly categorized as red but due to a large difference in the wavelengths both will not look same.          

The range of wavelengths roughly from 590 nm to 620 nm is seen as orange to human eyes. But the color of 620 nm and 621 nm light may not be differentiated by the human eyes. Because the range is roughly divided, the 620 nm light and 621 nm light will appear same.         

In the white light of Sun broadly seven colors are there. Violet, Indigo, Blue, Green, Yellow, Orange and Red (VIBGYOR), but a large number of shades of each of the colors can be distinguished by human eyes.

Since most of the diffracted light is distributed between an angle θ such that sinθ = -λ/b to sinθ = λ/b, where b is the slit width. As b is increased, θ decreases. It means the cone of divergence narrows down and the diffraction effects will be less clearly visible.

No. It is the frequency of the visible light that determines the color perception to the human eyes. It is so because the energy of a photon depends on the frequency and this energy of the photon determines a particular color.          

 It can be understood in another way. When we see a light, it enters our eyes through eye-lens and passes through the fluid in the eyeballs before reaching the retina. Whether we see the light of a certain frequency in the air or in water it has to go through the fluid in the eyeballs. In that fluid, this frequency will have the same corresponding wavelength. Hence the same color.

Since the wavelength of a light wave is very small in comparison to sound wave, diffraction effects are not noticeable and the light almost travels in a straight line. Hence the cardboard is opaque and we cannot see the light.

In the case of sound waves the diffraction, reflection and refraction are prominent so it can be heard. Sound waves not only bend near the end of cardboard but it can vibrate the cardboard which in turn vibrate the air molecules on the other side to propagate the sound.

(d) A laser .

EXPLANATION: 

The candle, bulb and mercury tube give lights of a mixture of wavelengths. In a laser, the same wavelength of light is processed and amplified. Hence the option (d).

(c) both particle and wave phenomenon.

EXPLANATION:   

The photoelectric effect shows it as a particle phenomenon while the interference and diffraction of light shows it as a wave phenomenon. Hence duel nature.