Question 126: Ray Optics

Question

Given is a thin convex lens of glass (refractive index $\mu$ ) and each side having radius of curvature $R$. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself?

Accepted Answer

We know, for a combination of a lens and a mirror,
$${P_{comb}} = 2{P_l} + {P_m}$$ ...... (1)
Also using lens maker formula,
$${1 \over {{f_l}}} = (\mu  - 1)\left( {{1 \over R} - {1 \over { - R}}} \right) = (\mu  - 1){2 \over R}$$
So using eq. (i),
$$ - {1 \over {{f_{comb}}}} = 2\left( {{1 \over {{f_l}}}} \right) - {1 \over {{f_m}}}$$
$$ \Rightarrow  - {1 \over {{f_{comb}}}} = {{4(\mu  - 1)} \over R} - {1 \over {\left( { - {R \over 2}} \right)}}$$
$$ \Rightarrow  - {1 \over {{f_{comb}}}} = {{4(\mu  - 1)} \over R} + {2 \over R}$$
$$ \Rightarrow  - {1 \over {{f_{comb}}}} = {2 \over R}(2\mu  - 2 + 1) = {2 \over R}(2\mu  - 1)$$
$$ \Rightarrow {f_{comb}} = {{ - R} \over {2(2\mu  - 1)}}$$
$$ \Rightarrow {R_{comb}} = 2{f_{comb}} = {{ - 2R} \over { - 2(2\mu  - 1)}} = {{ - R} \over {2\mu  - 1}}$$
Hence, distance $$ = {R \over {2\mu  - 1}}$$

Answer

$R / \mu$

Answer

$R /(2 \mu-1)$

Answer

$\mathrm{R} /(2 \mu-3)$

Answer

$\mu \mathrm{R}$

Ray Optics

Given is a thin convex lens of glass (refractive index \mu ) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself?

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