Question

The linear distance separating the headlights of a car is 1.1 m. Assuming light of 460 nm, a pupil diameter of 5.0 mm, and an average index of refraction for the eye of 1.36 . 24) What is the limiting angle of resolution

a) 0.33×10⁻⁶ rad
b) 92×10⁻⁶ rad
c) 1.22×10⁻⁶ rad
d) 112×10⁻⁶ rad
e) 82.5×10⁻⁶ rad

Answer 1

The limiting angle of resolution for the given conditions is option (e) 82.5× 10−6 rad.

Step-by-step explanation:

To calculate the limiting angle of resolution for the eye, we use the Rayleigh criterion formula: θ = 1.22 λ / D, where λ is the wavelength of light and D is the diameter of the aperture (in this case, the pupil of the eye). For the scenario where the linear distance separating the headlights of a car is 1.1 meters, the wavelength of light is 460 nm (460 × 10−6 m), and the pupil diameter is 5.0 mm (5.0 × 10−3 m), with the average index of refraction for the eye being 1.36, we can proceed with the calculation.

First, we convert the wavelength of light in the eye's medium by dividing it by the index of refraction: λ' = λ / n = 460 × 10−6 m / 1.36. We then apply the Rayleigh criterion formula to find the angle θ: θ = 1.22 × λ' / D.

By inserting the given values, we determine the limiting angle of resolution, θ:

• θ = 1.22 × (460 × 10−6 m / 1.36) / (5.0 × 10−3 m)
• θ = 1.22 × 338.2 × 10−9 m / 5.0 × 10−3 m
• θ = 1.22 × 0.06764 × 10−6 rad
• θ = 0.0825 × 10−6 rad (Option (e) 82.5× 10−6 rad)