Question

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

Answer 1

When a concave mirror is placed facing the sun, the sun rays converge to a point 10cm from the mirror. Thus the focal length of the mirror is 10cm.

radius of curvature = 2×f = 2×10 =20cm
Since the candle is placed at the centre of curvature, AN IMAGE OF SAME HEIGHT will be formed at the same place(CENTRE OF CURVATURE). Thus you have to place the screen at 20 cm from the mirror.
The image will be of same height as object. So it will be 2cm.

Draw the ray diagram for image when object is placed at 2f from the concave mirror.(from book)

Answer 2

Answer:

v = - 20

$\display \text{h _i = -2 cm}$

Explanation:

Given :

Focal length = 10 cm

Object distance = 20 cm

We have image formula :

1 / f = 1 / v + 1 / u

1 / v = 1 / - 10 + 1 / 20

1 / v = - 1  20

v = - 20.

Therefore , screen would be placed at distance of 20 cm to get image.

We have :

m = - v / u = h_i / h_o

- 20 / 20 = h_i / 2

h_i = - 2 cm.

Hence size of the image is 2 cm.