Question

The lens labelled (B) has radius 16.5cm on the curved side. Using the shape of the lens to assign the sign of the radius, calculate the focal length of the lens. Give your answer with the correct positive or negative sign using the usual convention for lenses.

Answer 1

convex f = 33 cm

concave f = -33 cm

Step-by-step explanation:

In geometric optics the focal length of a lens is given by

`(1)/(f) = ( n-1) \ ((1)/(R_2) - (1)/(R_1) )`

where n is the refractive index of the medium, R₁ and R₂ are the focal lengths on each side of the lens.

In this case one of the sides is flat so its focal length is infinite, if the lens is convex the focal length is positive, convergent lens and if it is concave the focal length is negative, divergent lens.

`(1)/(f) = (n-1) \ (1)/(R)`

the refractive index of the glass is n = 1.5

let's calculate

1 / f = (1.5 -1) 1 / 16.5

1 / f = 0.03030

f = 33 cm

convex f = 33 cm

concave f = -33 cm