A Young's double-slit experimental set up is kept in a medium of refractive index $\left(\frac{4}{3}\right)$. Which maximum in this case will coincide with the $6^{\text {th }}$ maximum obtained if the medium is replaced by air?

Assertion (A): In a Young's double-slit experiment, interference pattern is not observed when two coherent sources are infinitely close to each other.

Reason (R): The fringe width is proportional to the separation between the two sources.

In a Young's double-slit experiment, the screen is moved away from the plane of the slits. What will be its effect on the following?

(i) Angular separation of the fringes.

(ii) Fringe-width.

According to Huygens principle, the amplitude of secondary wavelets is

A beam of light travels from air into a medium. Its speed and wavelength in the medium are $$1.5 \times 10^8\mathrm{ms}^{-1}$$ and $$230 \mathrm{~nm}$$ respectively. The wavelength of light in air will be

Assertion (A) : In Young's double slit experiment all fringes are of equal width.

Reason (R) : The fringe width depends upon wavelength of light $$(\lambda)$$ used, distance of screen from plane of slits (D) and slits separation (d).

(a) (i) A plane light wave propagating from a rarer into a denser medium, is incident at an angle $i$ on the surface separating two media. Using Huygen's principle, draw the refracted wave and hence verify Snell's law of refraction.

(ii) In a Young's double slit experiment, the slits are separated by 0.30 mm and the screen is kept 1.5 m away. The wavelength of light used is 600 nm . Calculate the distance between the central bright fringe and the $4^{\text {th }}$ dark fringe.

OR

(b) (i) Discuss briefly diffraction of light from a single slit and draw the shape of the diffraction pattern.

(ii) An object is placed between the pole and the focus of a concave mirror. Using mirror formula, prove mathematically that it produces a virtual and an enlarged image.

(a) A plane wave-front propagating in a medium of refractive index '$$\mu_1$$' is incident on a plane surface making an angle of incidence (i). It enters into a medium of refractive index $$\mu_2\left(\mu_2>\mu_1\right)$$. Use Huygen's construction of secondary wavelets to trace the retracted wave-front. Hence, verify Snell's law of refraction.

OR

Using Huygen's construction, show how a plane wave is reflected from a surface. Hence, verify the law of reflection.

What happens to the interference pattern when two coherent sources are

(a) infinitely close, and

(b) far apart from each other

(a) (i) State Huygen's principle. With the help of a diagram, show how a plane wave is reflected from a surface. Hence, verify the law of reflection.

(ii) A concave mirror of focal length $$12 \mathrm{~cm}$$ forms a three times magnified virtual image of an object. Find the distance of the object from the mirror.

OR

(b) (i) Draw a labelled ray diagram showing the image formation by a refracting telescope. Define its magnifying power. Write two limitations of a refracting telescope over a reflecting telescope.

(ii) The focal lengths of the objective and the eyepiece of a compound microscope are $$1.0 \mathrm{~cm}$$ and $$2.5 \mathrm{~cm}$$ respectively. Find the tube length of the microscope for obtaining a magnification of 300.