A concave mirror Used for Rear view on an automabile has a radius of curvature of 8.00m .If a bus is located at 10.00m from the mirror find the position,nature and Size of the Image ?
Answers
Given :-
◉ We are given a concave mirror which is being used for rear view and has a radius of curvature 8.00 m. Object distance is u = -10 m.
To Find :-
◉ Position, Nature and Size of the image.
Solution :-
We know, Focal length of a spherical mirror is half the radius of the sphere it was made of.
So,
⇒ Focal Length = C/4 [ C = 2r ]
⇒ f = 8/4
⇒ f = 2.00 m
But, We know, Focal length of a concave mirror is always negative.
∴ f = - 2.00 m
Also, Object distance is always negative.
∴ u = -10.00 m
Now that we know the distance of the object and focal length of the mirror, we have
⇒ 1/f = 1/v + 1/u
⇒ -1/2 = 1/v - 1/10
⇒ 1/v = 1/10- 1/2
⇒ 1/v = 1 - 5/10
⇒ 1/v = -2/5
∴ v = -2.25 m
Now, Let us find the Magnification in order to know the characteristics of the image formed.
⇒ m = -v/u
⇒ m = -(-2.25/-10)
⇒ m = -2.25/10
⇒ m = -0.225
When a Magnification is negative that means the image formed is real and inverted.
Image Properties :-
- Size : 0.2 times the object size.
- Position : 2.25 m from the mirror.
- Nature : Real and Inverted.