Question

A plane convex lens of focal length 16 cm, is to be made of glass of refractive index 1.5. The radius of curvature of the curved surface should be(a) 8 cm(b) 12 cm(c) 16 cm(d) 24 cm

Answer 1

using mirror formula

$\frac{1}{v} - \frac{1}{u} = ( \gamma - 1)( \frac{1}{r1} - \frac{1}{r2} )$

where gamma = refractive index = 1.5

as lens is a plano convex therefore,

r1=-r2=r

consider a ray coming from infinity to the convex lens such that it image is formed at focus of the convex lens

therefore, 1/u= 1/infinity = 0

and 1/v= 1/foc. length = 1/16

$\frac{1}{16} = (1.5 - 1)( \frac{1}{r} - ( \frac{ - 1}{r} )) \\ \frac{r}{2} = 0.5 \times 16 \\ r = 16cm$

Answer 2

Answer:

a) 8cm

Explanation:

Focal length of the lens = 16cm (Given)

Refractive index of glass = 1.5 (Given)

Thus, According to the mirror formula, the equation will be -

1/f = (u-1)(1/R1-1/R2)

1/16 = (0.5-1) (1/R1-1/∞)

1/16 = 0.5×1/r

R = 8

Thus, the radius of curvature of the curved surface should be 8cm