 |
| Numerical - 08 |
|
| 08. (a) A screen is placed 90 cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. Determine the focal length of the lens. |
| |
| (b) Suppose the object in (a) above is an illuminated slit in a collimator tube so that it is hard to measure slit size and its distance from the screen. Using a convex lens, one obtains a sharp image of the slit on a screen. The image size is measured to be 4.6 cm. The lens is displaced away from the slit and at a certain location, another sharp image of size 1.7 cm is obtained. Determine the size of the slit. |
| |
| Suggested solution: |
| |
| (a) Distance between object and image, D = 90 cm |
| |
| Distance through which lens is displaced, d = 20 cm |
| |
| Now, D = u + v = 90 cm; d = u v = 20 cm |
| |
| \ u = 55 cm or 35 cm and v = 35 cm or 55 cm |
| |
| |
 |
| |
| (b) For first location of lens, u1 = x and v1 = y |
| |
| For second location of lens, u2 = y and v2 = x |
| |
| |
 |
| |
 |
| |
| or |
| |
 |
| |
