Question

8. Your nearsighted brother has a far point of 4 m and he wants to see an object 15 m away clearly Assume he will wear his glasses 2 cm in front of his eyes. What is the focal distance (in meters) of the glasses he needs? Hint: Draw a diagram of your brother, the glasses, the object and the image. Use the diagram to figure out whether the glasses have to be diverging or converging. 9. Consider question 8. What if, instead of an object 15 m away, he wants to see something far away clearly? What would be the focal distance then? 10. Your farsighted uncle has a near point of 2.5 m. He wants to be able to read at an arm's length (30 cm). Assume he will wear his glasses at a distance of 2.0 cm from his eyes. Hint: Draw a diagram of your brother, the glasses, the object and the image. Use the diagram to figure out whether the glasses have to be diverging or converging. What is the power (in diopters) of the glasses he needs? 11. Consider question 10. What if, instead of an object 15 m away, he wants to see something 1m away clearly? What would be the power then? 12. Lens combinations work because the first lens creates an image of the object and the second lens creates an image of that image. In order for a combination to work, the image formed by the first lens must be: 1. Real. 2. Virtual 3. Real or virtual, either works.

Answer 1

(sign convention: all distances are measured as distances measured in cartition coordinate such that lense is placed at the origin.) Calculate the focal distance of glass using following formula: 1 1 1 fvu Here, f is the focal distance, v is the image distance, and u is the object distance. To view the object placed at 15 m, the image should be formed at far point that is at 4 m from the eye. Calculate the distance of image from the glass. V = 4 m - 2 cm = 4 m - 0.02 cm = 3.98 m Image distance should be negative because it will be formed at the left side of the lense. Also, distance of object from the eye is 15 m hence, distance of object from the glass is 14.98 m. Now, calculate forcal distance. 1 1 1 U-1 (-3.98 m)(-14.98 m) (-14.98 m)-(-3.98 m) =-5.42 m

Focal length is negative, it indicates that the lense is diverging lense. 2 cm m 15 m In the above diagram, the ray which is parallel to the principle axis should appear to coming from frocal point which is shown by red colour. And the other ray which passes throught the optical centre goes undeviated.