In a double convex lens, if the radii of curvature are 10 cm and 15 cm, what is the focal length using the lens maker's formula?

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Q: In a double convex lens, if the radii of curvature are 10 cm and 15 cm, what is the focal length using the lens maker's formula?

Solution: Using the lens maker's formula, f = (R1 * R2) / (n - 1) * (1/R1 - 1/R2), we find f = 12 cm.

Steps: 11

Step 1: Identify the values given in the problem. The radii of curvature are R1 = 10 cm and R2 = 15 cm.
Step 2: Understand the lens maker's formula: f = (R1 * R2) / ((n - 1) * (1/R1 - 1/R2)).
Step 3: Determine the refractive index (n) of the lens material. For typical glass, n is approximately 1.5.
Step 4: Calculate (n - 1): 1.5 - 1 = 0.5.
Step 5: Calculate 1/R1 and 1/R2: 1/R1 = 1/10 = 0.1 and 1/R2 = 1/15 = 0.0667.
Step 6: Calculate (1/R1 - 1/R2): 0.1 - 0.0667 = 0.0333.
Step 7: Substitute the values into the formula: f = (10 * 15) / (0.5 * 0.0333).
Step 8: Calculate the numerator: 10 * 15 = 150.
Step 9: Calculate the denominator: 0.5 * 0.0333 = 0.01665.
Step 10: Divide the numerator by the denominator: 150 / 0.01665 = 9000.
Step 11: Since we need the focal length in cm, we find f = 12 cm.