Question 1
The lens maker's equation (1/f) = (n-1)(1/R₁ - 1/R₂) shows that the focal length of a plano-convex lens (R₂ = ∞, R₁ = R) is:
Af = R/(n-1)
Bf = R/2(n-1)
Cf = 2R/(n-1)
Df = (n-1)/R
Question 2
The critical angle θ_c for total internal reflection relates to the refractive index as:
An = sin θ_c
Bn = 1/sin θ_c
Cn = tan θ_c
Dn = cos θ_c
Question 3
The resolving power of a microscope is the minimum separation between two points that can be distinguished. It is given by the Rayleigh criterion as approximately:
Ad_min = λ/(2 n sinα)
Bd_min = λ n sinα
Cd_min = λ/(n sinα)
Dd_min = 2λ/sinα
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