Final answer:
The focal length of a plano-convex lens with a convex surface radius of 75 cm and an index of refraction of 1.6 is calculated to be 125 cm. However, since this is not an answer option, and assuming there is a typo, the closest option would be 100 cm.
Step-by-step explanation:
To find the focal length of a plano-convex lens, we use the Lensmaker's formula, which for a plano-convex lens simplifies to:
f = R / (n - 1), where:
- R is the radius of curvature of the convex surface,
- n is the index of refraction of the material.
Given that the convex surface radius R is 75 cm and the index of refraction n is 1.6, we can substitute these values into the formula to find the focal length f.
Thus, the calculation will be:
f = 75 cm / (1.6 - 1) = 75 cm / 0.6 = 125 cm
This value, however, is not listed among the options provided in the question. Therefore, it's possible that there was a typo either in the value of the radius provided in the question or in the answer options.
If we assume that it's a typo in the answers and we approximate to nearest options, then the closest answer would be d) 100 cm.