Lens Maker's Formula - Practice Questions & MCQ

Lens Maker's formula -

Derivation of Lens maker formula - 

Let us take a lens having refractive index = $\mu_2$ and the surrounding is having refractive index = $\mu_1$. Also, let us assume that the lens is having two refracting surfaces having radii R₁ and R₂. 

Here I' is the intermediate image and I is the final image.

As we have learned the formula of refraction at a single spherical surface. Let us apply this to the surface ACB, we get - 

$
\frac{\mu_2}{v_1}-\frac{\mu_1}{u}=\frac{\mu_2-\mu_1}{R_1} \ldots \text { (1) }
$

Similarly for the second surface ADB-

$
\frac{\mu_1}{v}-\frac{\mu_2}{v_1}=\frac{\mu_1-\mu_2}{R_2} \ldots \text { (2) }
$

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

Now adding equations (1) and (2),

$
\begin{aligned}
& \frac{\mu_1}{v}-\frac{\mu_1}{u}=\left(\mu_2-\mu_1\right)\left[\frac{1}{R_1}-\frac{1}{R_2}\right] \\
& \Rightarrow \frac{1}{v}-\frac{1}{u}=\left(\frac{\mu_2}{\mu_1}-1\right)\left[\frac{1}{R_1}-\frac{1}{R_2}\right]
\end{aligned}
$

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

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

we get,

$
\begin{aligned}
& \frac{1}{f}=\left(\frac{\mu_2}{\mu_1}-1\right)\left[\frac{1}{R_1}-\frac{1}{R_2}\right] \\
& \frac{\mathbf{1}}{\mathbf{f}}=\left(\mu_{\text {relative }}-1\right)\left(\frac{1}{\mathbf{R}_{\mathbf{1}}}-\frac{1}{\mathbf{R}_{\mathbf{2}}}\right)
\end{aligned}
$

Where,

$
\mu_{\text {relative }}=\frac{\mu_{\text {lens }}}{\mu_{\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 the same.