a needle is placed vertically at 12 cm from a concave mirror with focal length of 15 cm find the location of image
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Answers
Given :-
u = - 12 cm
f = + 15 cm
Solution :-
Using lens formula,
1/f = 1/u + 1/ve⇒ 1/v = 1/f - 1/u
⇒ 1/v = 1/15 - 1/- 12
⇒ 1/v = 60/9
⇒ v = 6.7 cm
Magnification, m = - (- v/u) = h₂/h₁
⇒ m = - 6.7/- 12
⇒ m = 0.558
m = h₂/h₁
h₂ = h₁ × m
⇒ h₂ = 0.558 × 4.5
⇒ h₂ = 2.5 cm.
As the needle is moved further from the mirror, image moves to the focus and the size of image goes on decreasing.
Answer:
h2 = 2.5 cm
Explanation:
Given: Height of the needle, h 1=4.5cm.
Object distance, u=−12cm.
The focal length of the convex mirror, f=15cm.
Image distance, v The value of v can be obtained using the mirror formula.
v/1+ u/1= f/1
v/1+ −12/1= 15/1
v/1= 12/1+ 15/1
v/1= 60/9
∴v=6.7cm
Hence, the image of the needle is 6.7 cm away from the mirror. Also, it is on the other side of the mirror.
The image size is given by the magnification formula.
m= h′/h = −/uv
h′= 6.7×4.5/12
⇒h′=+2.5cm
So, m=2.5/4.5
m=0.56
The height of the image is 2.5cm. The positive sign indicates that the image is erect, virtual, and diminished. If the needle is moved farther from the mirror, the size of the image will reduce gradually.