A plano-convex lens has a focal length f= 0.19 m. The radius of curvature of the convex side of the lens has been determined to be 0.08 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= 0.19 m. The radius of curvature of the convex side of the lens has been determined to be 0.08 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 = 0.19 m, R1 = ∞ (for the flat side), R2 = -0.08 m (the negative sign indicates that the center of curvature is on the same side of the lens as the light being considered).
Substituting these values into the lensmaker's formula:
1/0.19 = (n - 1) * (1/∞ - 1/-0.08)
Solving for n:
n = 1 + 0.19/0.08 = 1 + 2.375 = 3.375
Therefore, the refractive index of the lens is approximately 3.38 (rounded to two decimal places).
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