Question

The diameter of aperture of a plano-convex lens is $6\text{cm}$ and its maximum thickness is $3\text{mm}$. If the velocity of light in the material of the lens is $2\times {10}^8\text{m/s}$, its focal length is $($approximately$)$

• A. $10\text{cm}$
• B. $15\text{cm}$
• C. $30\text{cm}$
• D. $60\text{cm}$

Answer 1

The correct option is C $30\text{cm}$

Diagram of the given lens:


Refractive index, $\mu$ of medium =$\frac{C}{v}$

$\Rightarrow \mu =\frac{3\times {10}^8}{2\times {10}^8}=1.5$

Let, $R$ is radius of curvature of lens.

Using geometry, we can write,

$(R-3{)}^2+(30{)}^2=R^2$

$\Rightarrow R^2+9-6R+900=R^2$

$\Rightarrow 909=6R$

$\Rightarrow R=151.5\text{mm}=15.15\text{cm}$

Applying lens maker formula,

$\frac{1}{f_0}=(\mu -1)(\frac{1}{R}-\frac{1}{\infty })$

Substituting the value of $\mu$ and $R$,

$\Rightarrow \frac{1}{f_0}=0.5\times \frac{1}{15.15}$

$\Rightarrow f_0=30.30\approx 30\text{cm}$

Hence, the option $\left(c\right)$ is correct answer.