If the value of focal length is 40 cm so what is the value of object distance and image distance
Answers
Explanation:
Given: An object is placed at a distance of 40 cm on the principal axis of a concave mirror of radius of curvature 30 cm .
To find the distance by which the image move if the object is shifted towards the mirror through 15 cm
Solution:
As per the given criteria,
Radius of curvature, R=−30cm
So, the focal length, f=
2
R
=
2
−30
=−15cm
object distance, u=−40cm
Applying the lens formula, we get
f
1
=
v
1
+
u
1
⟹
(−15)
1
=
v
1
+
(−40)
1
⟹
v
1
=
(−15)
1
+
(40)
1
⟹
v
1
=
120
−8+3
⟹v=−24cm
The distance between the image and the mirror is 24cm when the object distance is 40cm.
Now, the object is moved 15cm towards the mirror, so the new object distance is u
′
=−(40−15)=−25cm
Now applying the lens formula we get,
f
1
=
v
′
1
+
u
′
1
⟹
(−15)
1
=
v
′
1
+
(−25)
1
⟹
v
′
1
=
(−15)
1
+
(25)
1
⟹
v
′
1
=
75
−5+3
⟹v=−37.5cm
is the new position of the image
So the shift in the position of the image is =40−37.5=2.5cm