how far should an object be placed from the pole of a concave spherical mirror of focal length 20 cm to form a real image of the size exactly 1/4th of the size of the object .
those who will give the proper answer , will be marked as brainliest one .
but those who will spam will be reported .
Answers
Answer: The object should be placed at a distance of 100 cm from the pole of concave mirror.
Given: the focal length of the mirror, f = 12 cm
To Find: the distance of the object, u.
Solution:
To calculate u, the formula used:
- 1 / f = 1/ v + 1 / u ⇒ Mirror formula
- here, f is the focal length of the concave mirror
u is the distance of the object from the mirror
v is the distance of the image from the mirror
Applying the above mirror formula:
1 /f = 1 / v + 1 / u
as per question-
v = (1/4)u
∴ - 1 / f = - ( 4/1 x u) - ( 1/u)
The negative sign is used for the real image as per the mirror sign convention rule.
-( 1/20) = - ( 4 / u) - (1 /u)
= - [ (4 / u) + ( 1/ u)]
= - ( 4+1 / u)
= - ( 5 / u)
- 1 / 20 = - 5 / u
Cancelling negative signs of bothe sides:
1 / 20 = 5 / u
( 1 / 20) x u = 5
u / 20 = 5
u = 5 x 20
= 100
u = 100 cm
Hence, the distance of the object from the mirror is 100 cm.