Question

a double convex lens having both faces of same radius of curvature has refractive index 1.55. Find out the radius of curvature of the lens required to get the focal length of 20cm.

Answer 1

Answer:

22 cm

Explanation:

According to the given question,

f = focal length = 20 cm

R = radius of curvature

u = refractive index = 1.55

And we are asked to find the radius of curvature.

We know,

• 1/f = (u-1)(1/R1-1/R2)

(Here R1 is positive and R2 is negative as it is double convex lens)

(And R1 = R2 = R)

• 1/f = (u-1)(1/R + 1/R)

• 1/f = 2(u-1)/R

• f = R/2(u-1)

• R = 2f(u-1)

(Putting the values)

• R = 2×20(1.55-1)

• R = 40×0.55

• R = 22 cm

So, Radius of curvature is 22 cm, to get the refractive index of 1.55 and focal length of 20 cm.