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

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

Solution: Using the lens maker's formula, the focal length is calculated to be 15 cm.

Steps: 8

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.