Sunday, May 05, 2013

JEE Main 2013 Questions on Geometric Optics

Science distinguishes a Man of Honor from one of those Athletic Brutes whom undeservedly we call Heroes.
– John Dryden (English poet, critic, dramatist)

The following questions on geometrical optics appeared in JEE Main 2013 question paper:
(1) Diameter of a plano - convex lens is 6 cm and thickness at the centre is 3mm. If speed of light in material of lens is 2 × 108 m/s, the focal length of the lens is :
(1) 15 cm
(2) 20 cm
(3) 30 cm
(4) 10 cm

In the adjoining figure the plano-convex lens is represented by ABCDA. The thickness of the lens is BD (which is equal to 0.3 cm) and the radius of the curved surface of the lens is R.
We have
            R2 = (R – 0.3)2 + 32
This gives R ≈ 15 cm.
The refractive index n of the material of the lens is the ratio of the speed of light in free space to the speed in the material of the lens:
             n = (3×108) /(2×108) = 1.5
The focal length f of the lens is given by the lens maker’s equation.
            1/f = (n – 1)(1/R  – 0)
[Since the second surface is plane, the reciprocal of its radius of curvature is zero]
Therefore 1/f = (1.5 – 1)(1/15) from which f = 30 cm
(2) The graph between angle of deviation (δ) and angle of incidence (i) for a triangular prism is represented by :

This is a very simple question. Most of you might have drawn the i - δ  curve by experimentally determining the values of δ for various values of i during your lab session. On increasing the angle of incidence i from a small value, the angle of deviation δ  decreases, attains a minimum value and then increases. The non-linear increase and decrease are in accordance with the relation,
            δ = i + e A where e is the angle of emergence and A is the angle of the prism.
The correct option is (3). 

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