Final answer:
The effective power of a cylindrical lens at different angles can be calculated using trigonometry. The powers of the lens at 20 degrees, 40 degrees, and 60 degrees from the base power of +3.00 D are approximately 2.64 D, 1.76 D, and 0.75 D respectively.
Step-by-step explanation:
The student question relates to calculating the power of a cylindrical lens at different angles from the plane perpendicular to the cylinder axis. Given a lens power of +3.00 diopters (D) with an axis at 90 degrees, the power at any other angle can be found using trigonometry, specifically using the cosines of the angles 20 degrees, 40 degrees, and 60 degrees.
For a cylindrical lens, the effective power (Peff) at any given angle (θ) from the axis is calculated using the formula Peff = P * cos^2(θ), where P is the original power of the lens.
- At 20 degrees: Peff = 3.00 D * cos^2(20°)
- At 40 degrees: Peff = 3.00 D * cos^2(40°)
- At 60 degrees: Peff = 3.00 D * cos^2(60°)
By substituting the cosine values for each angle, we obtain the effective power for each case:
- At 20 degrees: Peff ≈ 3.00 D * (0.9397)^2 ≈ 2.64 D
- At 40 degrees: Peff ≈ 3.00 D * (0.7660)^2 ≈ 1.76 D
- At 60 degrees: Peff ≈ 3.00 D * (0.5)^2 = 0.75 D