an image is three times the size of an object placed in front of a concave mirror of radius 30 cm calculate the object distance and size of the object
Answers
Answer :
There are two possible distances of object from the mirror:
(1) u = -20 cm to give real and inverted image
(2) u = -10 cm for virtual and erect image.
size of object will be always 1/3 of the size image.
Explanation :
Let,
- position of object = u
- position of image = v
- height of image = h₁
- height of object = h₂
- focal length of concave mirror = f
Given that ,
Radius of Curvature of concave mirror,R = -30
so, using formula R = 2 f
→ f = R /2
→ f = -30 / 2
→ f = -15 cm
Now, as given
image is 3 times the size of object
so there are 2 cases
(1) when image formed will be real , inverted and enlarged ,i.e ( magnification = -3) and
(2) when image formed will be virtual erect and inverted,i.e (magnification = 3)
therefore,
when image is real inverted and enlarged
→ magnification = -v / u
→ - 3 = -v /u
→ 3 = v /u
→ v = 3 u
now,
using mirror formula
→ 1/f = 1/v + 1/u
→ 1/(-15) = 1/3u + 1/u
→ 1/(-15) = (1+3)/(3u)
→ 1/(-15) = 4 /3u
→ 3 u = -60
→ u = -20 cm
so, In first case
When image formed will be real and inverted then position of image will be 20 cm in front of the mirror .
Now,
When image is virtual erect and enlarged
→ magnification = -v / u
→ 3 = -v /u
→ -v = 3 u
→ v = -3u
using mirror formula
→ 1/f = 1/v + 1/u
→ 1/(-15) = 1/(-3u) + 1/u
→ 1/(-15) = (-1+3)/(3u)
→ 1/(-15) = 2 / 3 u
→ 3 u = -30
→ u = -10 cm
Therefore,
●Two possible distances of object from the mirror are 20 cm and 10 cm in front of the mirror .
●In each case size of object will be 1/3 rd of the size of image.
●Nature of image will be real and inverted when u = -20 cm and Nature of image will be virtual and erect when object is placed at u = -10 cm.