Question 71: Ray Optics

Question

In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to $\left|R_1\right|$ and $\left|R_2\right|$, i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is

Accepted Answer

Using lens maker formula, $${1 \over f} = \left( {{{{\mu _2}} \over {{\mu _1}}} - 1} \right)\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$
Note : here, we will take air as medium for all three lenses so $${\mu _1} = 1$$
$${P_1} = {1 \over {{f_1}}} = \left( {{4 \over 3} - 1} \right)\left( {{1 \over \infty } - {1 \over { - {R_1}}}} \right)$$
$${P_1} = {1 \over 3}\left( {{1 \over {{R_1}}}} \right)$$ ..... (1)
$${P_2} = {1 \over {{f_2}}} = \left( {{3 \over 2} - 1} \right)\left( {{1 \over { - {R_1}}} - {1 \over { - {R_2}}}} \right)$$
$$ \Rightarrow {P_2} = {{ - 1} \over 2}\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$ .... (2)
$${P_3} = {1 \over {{f_3}}} = \left( {{4 \over 3} - 1} \right)\left( {{1 \over { - {R_2}}} - {1 \over \infty }} \right)$$
$$ \Rightarrow {P_3} = {{ - 1} \over 3}{1 \over {{R_2}}}$$ ...... (3)
So, $${P_{eq}} = {1 \over {3{R_1}}} - {1 \over 2}\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right) - {1 \over {3{R_2}}}$$
$$ = {1 \over 3}\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right) - {1 \over 2}\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$
$$ = \left( {{1 \over 3} - {1 \over 2}} \right)\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$
$${P_{eq}} = {{ - 1} \over 6}\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$

Answer

$-\frac{1}{6}\left(\frac{1}{\left|\mathrm{R}_1\right|}-\frac{1}{\left|\mathrm{R}_2\right|}\right)$

Answer

$-\frac{1}{6}\left(\frac{1}{\left|\mathrm{R}_1\right|}+\frac{1}{\left|\mathrm{R}_2\right|}\right)$

Answer

$\frac{1}{6}\left(\frac{1}{\left|\mathrm{R}_1\right|}+\frac{1}{\left|\mathrm{R}_2\right|}\right)$

Answer

$\frac{1}{6}\left(\frac{1}{\left|\mathrm{R}_1\right|}-\frac{1}{\left|\mathrm{R}_2\right|}\right)$

Ray Optics

In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to \left|R_1\right| and \left|R_2\right|, i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is

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