A biconvex lens has radii of curvature 20 cm and 30 cm. What is the focal length

A biconvex lens has radii of curvature 20 cm and 30 cm. What is the focal length of the lens?

A biconvex lens has radii of curvature 20 cm and 30 cm. What is the focal length of the lens?

Step 1: Identify the radii of curvature of the lens. In this case, they are R1 = 20 cm and R2 = 30 cm.
Step 2: Use the lens maker's formula, which is given by the equation: 1/f = (n - 1) * (1/R1 - 1/R2).
Step 3: Assume the lens is made of glass with a refractive index (n) of approximately 1.5.
Step 4: Substitute the values into the formula: 1/f = (1.5 - 1) * (1/20 - 1/30).
Step 5: Calculate (1/20 - 1/30). First, find a common denominator, which is 60. So, 1/20 = 3/60 and 1/30 = 2/60. Therefore, 1/20 - 1/30 = 3/60 - 2/60 = 1/60.
Step 6: Now substitute back into the formula: 1/f = 0.5 * (1/60).
Step 7: Calculate 0.5 * (1/60) = 1/120.
Step 8: Therefore, f = 120 cm. However, since we need the focal length, we take the reciprocal of 1/120, which gives us f = 15 cm.

Lens Maker's Formula – The formula used to calculate the focal length of a lens based on its radii of curvature and the refractive index of the material.
Biconvex Lens – A lens that is curved outward on both sides, which converges light rays that pass through it.
Radii of Curvature – The distances from the lens surface to the center of curvature, which affect the lens's focal length.