Name: Formation of Rainbow
Uploaded: 2019-07-19
Duration: 4 min 3 s
Description: Our joy knew no bounds when we used to see a rainbow in the sky in our childhood days. Kids! Do you know how a rainbow is formed? You can learn from this video.

Question

Derive an expression for a thin double convex lens. Can you apply the same to a double concave lens too?

Accepted Answer

Consider an object $O$ is placed at a distance $u$ is formed an image other side of the double convex lens at a distance $v$ .

$μ_{1}$ is the refractive index of the rarer medium and $μ_{2}$ is the refractive index of the denser medium. Such that $μ_{2} > μ_{1}$

We know that, refraction at spherical surface is $\frac{μ_{2}}{v} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R}$ (where $R$ is the radius of curvature)

Refraction at first surface,

$\frac{μ_{2}}{C I'} - \frac{μ_{1}}{(- O C)} = \frac{μ_{2} - μ_{1}}{C C_{1}}$ ........( $1$ )

Similarly, refraction on second surface,

$\frac{μ_{2}}{C I} - \frac{μ_{1}}{C I'} = \frac{μ_{2} - μ_{1}}{(- C C_{2})}$ ........( $2$ )

Adding both equations ( $1$ ) and ( $2$ ) we get,

$\frac{μ_{1}}{O C} + \frac{μ_{1}}{C I} = μ_{2} - μ_{1} (\frac{1}{C C_{1}} + \frac{1}{C C_{2}})$

$μ_{1} (\frac{1}{v} - \frac{1}{u}) = μ_{2} - μ_{1} (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$\frac{1}{f} = (\frac{μ_{2}}{μ_{1}} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$ $∵ (\frac{1}{f} = \frac{1}{v} - \frac{1}{u})$

$\frac{1}{f} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$ $∵ (μ = \frac{μ_{2}}{μ_{1}})$

This is the lens makers formula. The same equation we can apply for concave lens also.

Derive an expression for a thin double convex lens. Can you apply the same to a double concave lens too?

Important Questions on Ray Optics and Optical Instruments

Learn and Prepare for any exam you want !