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(a) Draw a ray diagram to show the image formation by a combination of two thin convex lenses in contact. Obtain the expression for the power of this combination in terms of the focal lengths of the lenses.
(b) A ray of light passing from air through an equilateral glass prism undergoes minimum deviation when the angle of incidence is
$\frac{3}{4}th$ of the angle of prism. Calculate the speed of light in the prism.

Answers (1)

For image $I_{1}$ by $L_{1}$

$\frac{1}{V_{1}}=\frac{1}{u}+\frac{1}{f_{1}}$

$\frac{1}{V_{1}}-\frac{1}{u}=\frac{1}{f_{1}}\; \; \; \; \; \; -----(1)$

For image $I$ by lens $L_{2}$

$\frac{1}{V}-\frac{1}{V_{1}}=\frac{1}{f_{2}}\; \; \; \; ------(2)$

$(1)+(2)$

$\Rightarrow \frac{1}{V}-\frac{1}{u}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$

Considering the two lens to be a single lens of focal length f then,

$\frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$

$\Rightarrow P=P_{1}+P_{2}$

$n=\frac{sin \frac{A+D_m}{2}}{sin(A/2)}$

$D_m=2i-A=2 \times \frac{3}{4}A-A=0.5A=30^0$

$n=\frac{sin(45)}{sin(30)}=\sqrt{2}$

$\frac{c}{v}=\sqrt{2}$

${v}=\frac{3\times10^8}{\sqrt{2}}=2.12\times 10^{8}\ m/s$

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Safeer PP

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