Lens Maker's Formula MCQ - Practice Questions with Answers

Lens Maker's formula -

Derivation of Lens maker formula - 

Let us take a lens having refractive index = n₂ and the surrounding is having refractive index = n₁. Also let us assume that the lens is having two refracting surface having radii R₁ and R₂. 

As we have learned the formula of refraction at a single spherical surface. Let us apply this on the surface (1), we get - 

$$\frac{n_2}{v_1}-\frac{n_1}{u}=\frac{n_2-n_1}{R_1}\dots (1)$$

Similarly for the second surface -

$$\frac{n_1}{v}-\frac{n_2}{v_1}=\frac{n_1-n_2}{R_2}\dots$$

Here, ${\mathrm{v}}_1$ is the position of image formed by the first surface and the same image will now act as object for the second surface.

Now adding equation (1) and (2),

$$\begin{array}{rl}& \frac{n_1}{v}-\frac{n_1}{u}=(n_2-n_1)[\frac{1}{R_1}-\frac{1}{R_2}]\\ & \Rightarrow \frac{1}{v}-\frac{1}{u}=(\frac{n_2}{n_1}-1)[\frac{1}{R_1}-\frac{1}{R_2}]\end{array}$$

Now we are going to arrange this equation in the desired for as -

$$\text{ So, put, }u=\mathrm{\infty }\text{ and }v=f$$

we get,

$$\frac{1}{f}=(\frac{n_2}{n_1}-1)[\frac{1}{R_1}-\frac{1}{R_2}]$$
 

$$\frac{1}{\mathbf{f}}=({\mu }_{\text{relative }}-1)(\frac{1}{{\mathbf{R}}_1}-\frac{1}{{\mathbf{R}}_2})$$

Where,

$${\mu }_{\text{relative }}=\frac{n_{\text{lens }}}{n_{\text{medium }}}$$
 

There are certain limitations of this lens maker’s formula - 

• The lens should not be thick so that the space between the two refracting surfaces can be small.
• The medium used on both sides of the lens should always be same.