Answer to Question #252413 in Optics for BsAkpadiaha

Question

A plano-convex lens of focal length 25.0 cm is to be made with crown glass of refractive index 1.52. Calculate the radius of curvature of the grinding and polishing tools to be used in making this lens.

Answer 1

Focal length of convex lens P=25.0 cm

Pefractive index of glass $\mu = 1.52$

The focal length of the thin lens is defined as the image distance for an object at infinity or the object distance for an image at infinity.

Therefore, lens maker’s formula

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

For a convex lens R₂ is flat so $\frac{1}{R_2} =0$

$\frac{1}{f} = (\mu-1) \times \frac{1}{R_1} \\ \mu = \frac{n_2}{n_1} \\ \frac{1}{f} = (1.52-1) \times \frac{1}{R_1} \\ R_1 = 25.0 \times 0.52 = 13 \;cm$

The radius of curvature is $R_1=13 \;cm$