An object is placed at a distance of 60cm from a convex mirror where the
magnification produced is 1/2. Where the object should be placed to get a magnification of 1/3 ?
Answers
Given :-
▪ An Object is placed at a distance of u = - 60 cm
from a convex mirror. The magnification produced is 1/2
To Find :-
▪ Distance at which the object should be put in order to get a magnification of 1/3.
Solution :-
The magnification is 1/3 which is given by,
⇒ m = -v / u
⇒ 1/2 = -v/-60
⇒ -60/2 = -v
⇒ v = +30 cm
Now that we have found the image and object distance, focal length of the mirror can be calculated as
⇒ 1/f = 1/u + 1/v
⇒ 1/f = -1/60 + 1/30
⇒ 1/f = (-1 + 2)/60
⇒ 1/f = 1/60
⇒ f = +60 cm
We had to find the object distance when the magnification is 1/3, so
⇒ m = -v / u
⇒ 1/3 = -v/u
⇒ v = - u / 3
⇒ 1/v = -3/u
Using the mirror formula, we have
⇒ 1/f = 1/v + 1/u
⇒ 1/60 = -3/u + 1/u
⇒ 1/60 = (-3 + 1)/u
⇒ 1/60 = -2/u
⇒ u = -120 cm
Hence, The object should be kept at a distance of 120 cm infront of the mirror.
➣Given:
- Object Distance, u = -60cm
- Magnification, m = 1/2 = 0.5
➣Find:
- Where should the object be placed
➣Solution:
we, know
Magnification is given by
Putting the values, we get
___________________
Now, using mirror formula,
Putting the values we get,
______________________
From, questioning for magnification, m = 1/3
Using the formula,
Putting the values we get,
______________________
Now, by using mirror formula
Putting the values we get,
Hence, the required object distance = 120cm