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Standard X

Physics

Lens Maker's Formula

In the figure...

Question

In the figure, light is incident on the thin lens as shown. The radius of curvature for both the surface is R. The focal length of this system is

f = \frac{μ_{3} R}{μ_{3} - μ_{1}}

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f = \frac{μ_{2} R}{μ_{1} - μ_{2}}

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f = \frac{μ_{3}}{μ_{2} - μ_{1}}

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f = \frac{μ_{1} R}{μ_{1} - μ_{2}}

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Solution

The correct option is D $f = \frac{μ_{1} R}{μ_{1} - μ_{2}}$
Consider refraction from the two spherical surfaces.
At surface 1,
$\frac{μ_{2}}{v_{1}} - \frac{μ_{1}}{\infty} = \frac{μ_{2} - μ_{1}}{R}$

At surface 2,
$\frac{μ_{3}}{v_{2}} - \frac{μ_{2}}{v_{1}} = \frac{μ_{3} - μ_{2}}{R}$

$⟹ v_{2} = \frac{μ_{3} R}{μ_{3} - μ_{1}} = f$

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In the figure, light is incident on the thin lens as shown. The radius of curvature for both the surface is R. The focal length of this system is

The correct option is D f=μ1Rμ1−μ2Consider refraction from the two spherical surfaces.At surface 1,μ2v1−μ1∞=μ2−μ1RAt surface 2,μ3v2−μ2v1=μ3−μ2R⟹v2=μ3Rμ3−μ1=f