If the radius of curvature of a lens is 30 cm, what is the focal length of the lens assuming it is made of glass with a refractive index of 1.5?

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Q: If the radius of curvature of a lens is 30 cm, what is the focal length of the lens assuming it is made of glass with a refractive index of 1.5?

Solution: Using the lens maker's formula, f = R/(n-1) = 30/(1.5-1) = 30/0.5 = 60 cm.

Steps: 8

Step 1: Identify the radius of curvature (R) of the lens, which is given as 30 cm.
Step 2: Identify the refractive index (n) of the lens material, which is given as 1.5.
Step 3: Use the lens maker's formula: f = R / (n - 1).
Step 4: Substitute the values into the formula: f = 30 / (1.5 - 1).
Step 5: Calculate the denominator: 1.5 - 1 = 0.5.
Step 6: Substitute the denominator back into the formula: f = 30 / 0.5.
Step 7: Perform the division: 30 divided by 0.5 equals 60.
Step 8: Conclude that the focal length (f) of the lens is 60 cm.