An object of height 4 cm is placed at a distance of 15 cm in front of a concave lens of power, -10
diopters. Find the size of the image.
Answers
Answer:
Object distance, u=−27cm
Radius of curvature of the concave mirror, R=−36cm
focal length of mirror f=R/2=−18cm
The image distance can be obtained using the mirror formula,
v
1
+
u
1
=
f
1
From above equation, v=−54cm.
Therefore, the screen should be placed 54 cm away from the mirror to obtain a sharp image. The magnification of the image is given as,
m=
h
h
′
=−
u
v
∴h
′
=−5cm
The height of the candle’s image is 5 cm. The negative sign indicates that the image is inverted and virtual. If the candle is moved closer to the mirror, then the screen will have to be moved away from the mirror in order to obtain the image.
Explanation:
The size of the candle (object) is , the distance of the candle (object) from the mirror is and the radius of curvature is .
The formula of the mirror is given as,
Where, the distance of the object is , the distance of the image is , the radius of curvature is and the focal length is .
By substituting the values in the above formula, we get
The negative sign indicates that the image is formed in front of the mirror.
Thus, the image is formed at at the front of the mirror.
The magnification is given as,
Where, the object height is and the image height is .
By substituting the values in the above expression, we get
Thus, the image formed is inverted and real. As, the candle is moved closer to mirror the screen would have to be moved farther.
When the candle closer than from the mirror, the image would be virtual and therefore cannot be collected on the screen.