Question

Angular Magnification and the Simple Magnifier Thomas wants to use his 5.5 -D reading glasses as a simple magnifier. What is the angular magnification of this lens when Thomas's eye is relaxed?

Short answer

Answer: The angular magnification of the 5.5-D reading glasses when Thomas's eye is relaxed is approximately 2.374.

Step-by-step solution

Convert the lens power to the focal length

To find the focal length of the lens, use the formula: Focal length (f) = 1 / Power (P) where Power (P) is given in diopters. In this case, the power of the reading glasses is 5.5 D. So, the focal length can be calculated as: f = 1 / 5.5

Calculate the focal length

Calculate the focal length by dividing 1 by 5.5: f = 1 / 5.5 f ≈ 0.182 m

Find the angular magnification

To find the angular magnification (M) of the lens when Thomas's eye is relaxed, use the formula for a simple magnifier: M = 1 + (D / f) where D is the nearest clear vision distance, which is typically 25 cm or 0.25 m. Now we can substitute the values into the formula to calculate the angular magnification.

Calculate angular magnification

Substitute the values for D and f into the formula: M = 1 + (0.25 / 0.182) M ≈ 1 + 1.374 M ≈ 2.374 The angular magnification of the 5.5-D reading glasses when Thomas's eye is relaxed is approximately 2.374.