Question

Parallel rays striking a spherical mirror far from the optic axis are focussed at a different point than are rays near the axis thereby the focus moves toward the mirror as the parallel rays move toward the outer edge of the mirror. What value of incidence angle θ produces a 2% change in the location of the focus, compared to the location for θ very close to zero?

Options

• 3.5°

• 5.5°

• 8.5°

• 11.5°

Answer 1

11.5°

Explanation:

f = PF = R - `"R"/2` secθ

for θ = 0, f = `"R"/2` 

0.98 f = R - `"R"/2` secθ

⇒ 0.98 f = `"R"/2` (2- secθ)

⇒ 0.98 = 2 - secθ

⇒ secθ = 1.02

⇒ cosθ ≃ 0.98

⇒ 1 - `theta^2/2` = 0.98

⇒ θ = 0.2 radian

= `(0.2xx180)/pi` ≃ 11.5°