A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?
Given,
Size of the candle, h = 2.5 cm
Object distance, u = –27 cm
Image size = h’ = ?
Radius of curvature of the concave mirror,
R = – 36 cm
Now focal length f is given as f = R/2
∴ f = R/2 = -18 cm
The image distance can be obtained using the mirror equation,
Where,
f is the focal length
u is object distance and
v is the image distance
⇒ 
⇒ 
⇒ 
⇒ v = -54 cm
Therefore, the screen should be placed at a distance of 54 cm
from the mirror to obtain a sharp image.
The magnification is given by
Where,
m is the magnification
h’ is the height of the image
h is the height of the object
v is the image distance
u is the object distance
Using the equation, we get,
⇒ 
⇒ h’ = -5 cm
∴ The height of the image is 5cm. The negative sign indicate that the image is real, inverted and magnified.
As the candle is moved closer to the mirror : | |
1) u > f | Then the screen should be moved farther away from the mirror. |
2) u < f | The image is virtual. |