A concave mirror of focal length 10 cm is placed in front of an object find the positions of the object for which image size is thrice that of size of the object?
Answers
Answer :-
Position of the object is 6.67 cm from the mirror.
Explanation :-
We have :-
• Focal length of the mirror = 10 cm
• Size of the image is thrice the size of the object.
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According to the question :-
→ hᵢ = 3hₒ
We know that :-
m = -(v/u) = hᵢ/hₒ
⇒ -(v/u) = 3hₒ/hₒ
⇒ -(v/u) = 3
⇒ v/u = -3
⇒ v = -3u
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Since the mirror is concave, we have :-
→ f = -10 cm
According to mirror formula :-
1/v + 1/u = 1/f
⇒ 1/(-3u) + 1/u = 1/(-10)
⇒ -1/3u + 1/u = -1/10
⇒ [-1 + 3]/3u = -1/10
⇒ 2/3u = -1/10
⇒ 3u(-1) = 2(10)
⇒ -3u = 20
⇒ u = 20/-3
⇒ u = - 6.67 cm
Answer:
Given :-
A concave mirror of focal length 10 cm is placed in front of an object
To Find :-
Position
Solution :-
Since the size of of image is trice So,
hi = 3 × ho = 3ho
Magnification = -v/u = hi/ho
-v/u = hi/ho
Putting hi as 3ho
-v/u = 3ho/ho
v/u = -3ho/ho
Cancellation of ho
v/u = -3
By cross multiplication
v = -3 × u
v = -3u
By using mirror formula
1/f = 1/u + 1/v
1/-10 = 1/u + 1/-3u
-1/10 = 1/u + -1/3u
-1/10 = 3 + (-1)/3u
-1/10 = 3 - 1/3u
-1/10 = 2/3u
By cross multiplication
-1(3u) = 10(2)
-3u = 20
-u = 20/3
u = -20/3
u = -6.67 cm