Question

When a concave mirror is placed facing the sun the sun rays converge to a point 10 cm from the mirror.now if you place 2 cm long candles flame 20 cm away on the principal axis of the mirror ,where would you place screen to obtain the image of the candle ? What would be the size of the image ? Draw a ray diagram to jastify your answer .

Answer 1

Given that a concave mirror converges the sun rays at a point 10cm from the mirror.

Hence the focal length of the concave mirror is
= 10 cm

f = -10 cm
u = -20 cm
h₁ = 2 cm

Using mirror formula ;

(1/f) = (1/v)+(1/u)
1/-10 = (1/v) - (1/20)
(1/v) = (1/20)-(1/10)
1/v = -1/20

v = -20 cm
____________________

m = -v/u = h₂/h₁
-(-20)/(-20) = h₂/2
h₂ = -2 cm
_____________________
Hence we will place the screen at 20cm from the mirror to obtain the image.
And the size of the image is 2cm ,i.e equal but inverted

Answer 2

when the light rays are coming from infinity then they will meet at the focus, as they said that it met at 10cm away from the mirror the focus is 10cm. as they said that the candle is placed at 20cm which is the centre of curvature of the mirror.
when an object is placed at the centre of curvature then the image is formed on the centre of curvature itself with the same size . so the screen must be placed on the centre of curvature for the image to be formed. as the object size = image size , size of the image is 2cm .