an object of height 5 cm is placed at a distance of 2m in front of a mirror and its image is obtained on a screen.Find the distance of screen from the mirror,nature of the mirror and its focal length.
To find the distance of the screen from the mirror, nature of the mirror, and its focal length, we can use the mirror formula. The formula is as follows:
1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror
- v is the image distance from the mirror
- u is the object distance from the mirror
Given:
- Object distance, u = 2m = 200cm
- The image height and object height are the same, h = 5cm; this implies that the image is of the same size as the object
Since the image is formed on the screen:
- Image distance, v = distance from the mirror to the screen
Substituting the given values into the mirror formula:
1/f = 1/v - 1/u
1/f = 1/v - 1/200
Since the image is neither magnified nor diminished in size, the magnification (m) is equal to 1:
m = h'/h = v/u
1 = v/200
v = 200 cm
Substituting v = 200 cm into the mirror formula:
1/f = 1/200 - 1/200
1/f = 0
f = infinity
From the calculation, we can deduce that the distance of the screen from the mirror is 200 cm, the nature of the mirror is a plane mirror (as the focal length is infinity), and the focal length of the mirror is infinity.