Question 178: Ray Optics

Question

A planoconvex lens becomes an optical system of $$28$$ $$cm$$ focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A.
If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig-B, it acts like an optical system of focal length $$10$$ $$cm.$$ The refractive index of the material of lens is :

Accepted Answer

When plane durface is silvered then focus length of lens,
f
1
= $${R \over {2\left( {\mu  - 1} ight)}}$$
and when curver surface is silvered then focus length  of lens,
f
2
= $${R \over {2\mu }}$$
$$	herefore\,\,\,\,$$ $${{{f_1}} \over {{f_2}}} = {R \over {2\left( {\mu  - 1} ight)}} 	imes {{2\mu } \over R}$$
$${\mu  \over {\left( {\mu  - 1} ight)}}$$
given f
1
= 28 and  f
2
= 10
$$	herefore\,\,\,\,$$ $${{28} \over {10}} = {\mu  \over {\mu  - 1}}$$
$$ \Rightarrow $$$$\,\,\,\,$$ 28$$\mu $$ $$-$$ 28 = 10 $$\mu $$
$$ \Rightarrow $$$$\,\,\,\,$$ 18 $$\mu $$ = 28
$$ \Rightarrow $$$$\,\,\,\,$$ $$\mu $$  = $${{28} \over {18}}$$ = 1.55

Answer

$$1.50$$

Answer

$$1.55$$

Answer

$$1.75$$

Answer

$$1.51$$

Ray Optics

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