﻿ The thickness of a plano-convex lens is 4 cm. When it is placed on a horizontal table in such a way that its curved surface be in contact with the table, then the depth of a bottom-point of the lens appears 3 cm. If the lens is inverted so that its plane surface be in contact with the table, then the apparent depth of the centre of the lens-surface is found to be (25/8) cm. Determine the focal-length of the lens.      : Kaysons Education

# The Thickness Of A Plano-convex Lens Is 4 Cm. When It Is Placed On A Horizontal Table In Such A Way That Its Curved Surface Be In Contact With The Table, Then The Depth Of A Bottom-point Of The Lens Appears 3 Cm. If The Lens Is Inverted So That Its Plane Surface Be In Contact With The Table, Then The Apparent Depth Of The Centre Of The Lens-surface Is Found To Be (25/8) Cm. Determine The Focal-length Of The Lens.

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## Question

### Solution

Correct option is

75 cm

In the first position, the curved surface of the lens is in contact with the table. Let the contact-point O be an object. The light rays starting from O, after refraction in air at the plane surface of the lens, forms virtual image Iof the object O. Now, as given, we have

Putting these values in the formula for refraction at a surface

Here the refracting surface is plane whose radius R = ∞.

or                           n = 3/4.

Since light-rays are going form glass to air; here n is refractive index of air with respect to glass (n = gna = 3/4).

In the second position, the plane surface of the lens is in contact with the table. Now, the virtual image I of the centre O of the plane surface of the lens is formed due to refraction at the curved surface of the lens. Again, as given

u = CO = – 4 cm and v = CI = –(25/8) cm and n = 3/4

(calculated above)

Let R be the radius of the curved surface of the lens.

Putting the values of uv and n in the formula

or

or

or                           R = –25 cm.

The focal length f of the lens in air is given by

Where n is refractive index of glass of lens with respect to air.

Here

or f = 75 cm.

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