OPTICS - MULTIPLE CHOICE QUESTION: Two converging lenses, of exactly the same si

Question

OPTICS - MULTIPLE CHOICE

QUESTION: Two converging lenses, of exactly the same size and shape, are held in sunlight, the same distance above a sheet of paper. The figure below shows the paths of some of the rays through the two lenses. Which lens is made of material with a higher index of refraction, and how do you know?

i. Lens 1, because its focal length is smaller.

ii. Lens 1, because its focal length is greater.

iii. Lens 2, because its focal length is smaller.

iv. Lens 2, because its focal length is greater.

v. Impossible to answer with the information given.

PLEASE EXPLAIN YOUR REASONING QUICKLY

Explanation / Answer

the relationship between refractive index and focal length appears in lens makers formula


1 / f = (n of lens / n of surrounding - 1)(1/r1 - 1/r2)

n of lens -> refractive index of lens

n of surrounding -> refractive index of surrounding

f -> focal length of lens

r1 -> the radius of curvature of first surface( on which light falls first )

r2 -> the radius of curvature of second surface

but this formula is valid for thin lens only

so the answer is

i. Lens 1, because its focal length is smaller.

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