A plano-convex lens has a focal length f= 0.18 m. The radius of curvature of the convex side of the lens has been determined to be 0.07 m and the radius of curvature of the flat side is assumed to be infinite.Calculate the refractive index of the lens. Express answer to two decimal places.
Question
A plano-convex lens has a focal length f= 0.18 m. The radius of curvature of the convex side of the lens has been determined to be 0.07 m and the radius of curvature of the flat side is assumed to be infinite.Calculate the refractive index of the lens. Express answer to two decimal places.
Solution
The refractive index (n) of the lens can be calculated using the lensmaker's formula:
1/f = (n - 1) * (1/R1 - 1/R2)
where: f is the focal length, R1 is the radius of curvature of the first surface, R2 is the radius of curvature of the second surface.
Given: f = 0.18 m, R1 = 0.07 m (convex side, so the value is positive), R2 = ∞ (flat side, so the value is negative).
Substituting R2 = ∞ into the lensmaker's formula, we get:
1/f = (n - 1) * (1/R1)
Rearranging the formula to solve for n, we get:
n = 1 + f/R1
Substituting the given values into the formula, we get:
n = 1 + 0.18/0.07
Calculating the above expression, we get:
n = 3.57
Therefore, the refractive index of the lens is 3.57.
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