Question

Velocity of light in glass is $2\times {10}^{8}m/s$. From the glass cocvexo-convex lens is prepared whose radius of curvatures are $15cm$ and $45cm$ respectively. A parallel beam of light is incident on the lens. The beam will converge at a distance of

• A. $15cm$
• B. $22.5cm$
• C. $60cm$
• D. $45cm$

Answer 1

The correct option is B $22.5cm$

$\begin{array}{cc}\text{Refractive index}& =\frac{\text{velocity of (air) light}}{\text{of glass}}\\ & =\frac{3\times {10}^8}{2\times {10}^8}\\ & \mu =\frac{3}{2}\end{array}$

Parallel beam of light will converge at

focus so we need to find focal length

$\begin{array}{c}\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})\\ \frac{1}{f}=(\frac{3}{2}-1)\left(\frac{1}{-15}\frac{1}{-45}\right)\\ f=22.5\\ \text{So option}B\text{is correct}\end{array}$