A double convex lens made of glass of refractive index 1.5 has both radii of curvature of magnitude 20 cm. An object 2 cm high is placed at 10 cm from the lems. Find the position, nature and size of the image.

In the normal adjustment of an astronomical telescope, the distance between the objective lens and the eye lens is 10 sm. The magnifying power of the telescope is 4. Calculate the focal lengths of objective and eye lens.

A breaker is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the beaker is measured by a microscope to be 9.4 cm. What is the refractive index of water ? If  water is If water is replaced by a liquid of refractive index 1.63 upto the same height, by what distance would the microscope have to be moved to focus on the needle again ?

Explain how corpuscular theory predicts the speed of light in a medium, say water, is greater than the speed of light in vacuum. Is the prediction confirmed by experimental determination of the speed of light in water? If not, which alternative picture of light is consistent with experiment?

In a Young's double slit experiment the slits are separated by 0.3 mm and the screen is placed 1.5m away. The distance between the central and 4th bright fringe is 1cm. Calculated the wavelength of light.

A ray of light is incident on one face of Ii glass prism and emerges out from the other face. Trace the path of the ray and derive an expression for refractive index of the glass prism.

Unpolarised light of intensity 10 passes through two polaroids P₁ and P₂ such that pass axis of P₂ makes an angle e with the pass axis of P₂. Plot a graph showing the variation of intensity of light transmitted through P₂ as the angle e varies from 0° to 180°.
A third polaroid P₃ is placed between Pl and P2 with pass axis of Ps making angle \(\beta\) with that of P₁ and the angle between P₁ and P₂ is \(\theta\). If l1, I₂ and I₃ represents the intensities of light transmitted by P₁, P₂ and P₃, then determine the values of angle \(\theta\) and \(\beta\) for which I₁ = I₂ = I₃.

A beam of unpolarised light is incident on the boundary between two transparent media. If the reflected light is completely plane polarised, how is its direction related to the direction of the corresponding refracted light? Define Brewster's angle. Obtain the relation between this angle and the refractive index for the given pair of media.

Explain by drawing a suitable diagram that the interference pattern in a double slit is actually a superposition of single slit diffraction from each slit.
Write two basic features which distinguish the interference pattern from those seen in a coherently illuminated single slit

(a) Good quality sun-glasses made of polaroids are preferred over ordinary coloured glasses. Justifying your answer.
(b) Two polaroids P₁ and P₂ are placed in crossed positions. A third polaroid P₃ is kept between P₁ and P₂ such that pass axis of P₃ is parallel to that of P₁ How would the intensity of light 10 transmitted through P₂ vary as P₃ is rotated? Draw a plot of intensity '\(\theta\)' Vs the angle 'e', between pass axes of P₁ and P₃.

Show that a convex lens produces an N times magnified image when the objet distances, from the lens, have magnitudes (f ± f / N). Here f is the magnitude of the focal length of the lens. Hence find the two values of object distance, for which a convex lens, of power 2.5D, will produce am image that is four times as large as the object?

Use the lens equation to deduce algebraically what you know otherwise from explicit ray diagrams.
(a) An object placed within the focus of a convex lens produce a virtual and enlarged image.
(b) A concave lens produces a virtual and diminished image independent of the location of the object

A beam of white light on passing through a hollow prism gives no spectrum. Why?

(a) A point object is placed in front of a double convex lens (of refractive index n =n₂/n₁ with respect air) with its spherical faces of radii of curvature R₁ and R_2.. Show the path of rays due to surface to obtain the formation of the real image of the object.
Hence obtain the lens maker's formula for a thin lens.
(b) A double convex lens having both faces of the same radius of curvature has refractive index 1.55. Find out the radius of curvature of the lens required to get the focal length of 20 cm.