Question

When a concave mirror is placed facing the sun, the sun's rays converge to a point 10 cm from the mirror. Now, an erect, 2-cm-long pin is placed 15 cm away on the principal axis of the mirror.
If you want to get the image of the pin on a card, where would you place the card?
What would be the nature and height of the image?

Answer 1

Concave mirror converges the rays of light to the point know as principal focus of the mirror.
Hence the focal length of the concave mirror is 10 cm

f = -10 cm
h₁ = +2 cm
u = -15 cm
h₂ & v = ?

Using mirror formula ;

1/f = 1/v + 1/u

(1/-10) = (1/v) + (1/-15)
1/v = (1/15) - (1/10)
1/v = (2-3)/30
v = -30
_________________________
Hence in order to get the image of a pin on a card, the card should be placed 30 cm in front of a concave mirror.
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m = (-v/u) = h₂/h₁

-(-30/-15) = h₂/2
h₂ = -4 cm
_________________________
The nature of image is Real, inverted and magnified i.e four times that of object.
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Answer 2

Answer:f = -10 cm ( since rays coming from infinity meet at focus using a concave mirror

u = -20 cm

Since candle flame is placed at the centre of curvature [as object distance is 20 cm which is twice of focal length i.e. center of curvature C], so the image will be formed at C. So screen will be placed 20 cm from the mirror on the same side of the object. Size of the image will be same as the size of object = 2 cm.

 

Explanation: