A convex lens is made from glass with an index of refraction

A convex lens is made from glass with an index of refraction n = 1.5 and radii of curvature 10cm and 6 2/3 cm. Calculate the focal length for this lens. This lens is placed 15 cm in front of a convex mirror with a 20 cm radius of curvature. Light from an object 20 cm in front of the lens passes through the lens, reflects off the mirror and passes through the lens again. Determine the image from the lens (first pass), mirror and lens (second pass). Solve this problem 2 ways: With the thin lens equation and With a scaled, carefully drawn ray diagram from which the answer is measured with a ruler.

Solution

1/f = (n-1)(1/R₁ + 1/R₂)

1/f = (1.5 - 1)(3/20 - 1/10)

1/f = 0.5 x (1/60) = 1/120

f = 400 cm