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Optics and Eyeglasses

1. A eyeglass lens has strength of +5.50 diopters. What is the focal length of the lens?
2. A farsighted eye has a near point of 150 cm. Objects closer than 150 cm are not seen clearly. A converging lens is used to permit clear vision of a book placed 25 cm in front of the eye. Find the focal length of the lens and express its strength in diopters?
3. A myopic person wears eyeglasses with a lens strength of -2.5 diopters. Where is the far point for that person's eyes?
4. The prescription for a student's eyeglasses is changed from 0.25 diopters to 1.25 diopters. By what distance had the student's near point shifted?
5. A 8X magnifying glass is placed 4.0 cm away from a postage stamp. (a) Where is the image of the stamp? (b) Is it real or virtual?
6. You are taking photos with a shutter speed of 1/500 s and a lens aperture of f/1.4. If you then set the lens to f/2.8, what should be the shutter speed to give the same exposure to the film?
7. The lens of a projection TV system has a maximum aperture of 5.8cm and is rated f/4.3. In operation, the lens of the image is 150 cm. What is the approximate diagonal size of the object element in the projection system? Note: The image is formed at 450 cm from the lens.
8. A 17.9-cm focal-length lens is used to project 35-mm slides onto a screen 4.27 m from the projector lens. What must be the size of the screen if the image of the slide is to just fill the screen? The dimensions of the image on the slide are 23.5 mm X 34.3 mm.
9. An eyepiece of 2.5-cm focal length and an objective of 0.32-cm focal length are used in a standard microscope. (a) What power should be marked on each element? (b) What is the overall magnification of the combination? Assume L is 16 cm.

Solution Preview

Power = +5.50 diopters
Focal length f = 1/5.5 m = 100/5.5 cm = 18.18 cm --Answer

image v = -150 cm
object u = -25 cm
focal length f = ?
1/f = 1/v - 1/u
=> 1/f = (-1/150) - (-1/25) = (-1 + 6)/150
=> f = 150/5 = 30 cm --Answer

Power of the specs glasses P = -2.5 diopters
focal length f = -1/2.5 m = -100/2.5 = -40 cm --Answer
-ve means concave lens of focal length 40 cm.

P1 = 0.25 diopters
=> f1 = 100/0.25 = 400 cm
u1 = -25 cm
v1 = ?
1/f = 1/v - 1/u
=>1/400 = (1/v1) - (-1/25)
=> 1/v1 = (1/400) - (1/25) = (1-16)/400
=> v1 = ...

Solution Summary

Solution contains formula, including 1/f = 1/v - 1/u, and calculations and answers.