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Q.

A lens forms a sharp image on a screen on keeping a parallel sided transparent slab between the lens and screen, it is found necessary to move the screen through a distance ‘x’ in order for the image to be again sharply focused. If thickness of the slab is ‘t’. then refractive index of the material of the slab is

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a

\frac{t - x}{t}

b

\frac{t}{x}

c

\frac{t}{t - x}

d

\frac{x}{t}

answer is C.

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Detailed Solution

Thickness of slab = t

$shift = (1 - \frac{1}{μ}) t$

$x = (1 - \frac{1}{μ}) t$

$x = (\frac{μ - 1}{μ}) t$

$μ x = μ t - t$

$t = μ t - μ x$

$t = μ (t - n)$

$μ = \frac{t}{t - x}$

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A lens forms a sharp image on a screen on keeping a parallel sided transparent slab between the lens and screen, it is found necessary to move the screen through a distance ‘x’ in order for the image to be again sharply focused. If thickness of the slab is ‘t’. then refractive index of the material of the slab is