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Chapter 16: Problem 2261

A plano convex lens off \(=20 \mathrm{~cm}\) is silvered at plane surface New f will be \(\quad \mathrm{cm}\) (A) 20 (B) 40 (C) 30 (D) 60

Short Answer

Expert verified
The new focal length of the plano-convex lens after silvering is \(40\) cm (option B). This is because the silvered surface causes internal reflection, effectively making the light pass through the lens twice and forming a virtual image at twice the original focal length.

Step by step solution

01

Understand the effect of silvering on plano-convex lens

When the plane surface of a plano-convex lens is silvered, the light entering the lens will be internally reflected by the silvered surface. This internal reflection causes the light to effectively pass through the lens twice, forming a virtual image at twice the original focal length.
02

Apply the lens formula

The lens formula is given by: \(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\) , where \(f\) is the focal length of the lens, \(v\) is the distance of the image from the lens, and \(u\) is the distance of the object from the lens. Since the image and object are at the same distance (due to internal reflection), we can replace \(v\) and \(u\) with \(x\), and the equation becomes: \(\frac{1}{f} = \frac{1}{x} - \frac{1}{x}\)
03

Obtain the new focal length

Given that the original focal length of the lens is \(20\) cm, the light effectively passes through the lens twice, doubling the distance between the lens and the virtual image. Therefore, the new focal length, denoted by \(f'\), can be obtained by multiplying the original focal length by 2: \(f' = 2f = 2 (20 \mathrm{~cm}) = 40 \mathrm{~cm}\)
04

Choose the correct answer

The new focal length of the plano-convex lens after silvering is \(40\) cm. So the correct option is (B) 40 cm.

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Most popular questions from this chapter

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