Question

A double convex lens is made of glass (n=1.50) and has a radius of 40 cm on the front side and 30 cm on the back side. What is the focal length of the lens?

Answer 1

The focal length of the double convex glass lens with radii of curvature 40 cm and 30 cm is 60 cm.

Step-by-step explanation:

The focal length of a lens can be determined using the lens maker's equation:

1/f = (n - 1) * (1/R1 - 1/R2)

Where f is the focal length, n is the refractive index of the lens material, R1 is the radius of curvature of the front surface, and R2 is the radius of curvature of the back surface. In this case, the radius of curvature of the front surface is 40 cm and the radius of curvature of the back surface is -30 cm (negative because it is concave). The refractive index of glass is 1.50. Plugging in these values into the lens maker's equation, we get:

1/f = (1.50 - 1) * (1/40 - 1/(-30))

Simplifying the equation gives:

f = 60 cm

Therefore, the focal length of the lens is 60 cm.