In a convex mirror when the object is kept at a distance of 30cm from the mirror the image is formed at a distance of 10cm from the mirror.What will be the change in the image distance if the object distance is doubled
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Answer:
When an object is kept at a distance of 30 cm from a convex mirror the image is found to be at a distance of 10 cm from the mirror.
The mirror formula is 1u+1v=1f, where,
u is the distance of the object from the mirror,
v is the distance of the image from the mirror, and,
f is the focal length of the mirror,
In a convex mirror we get a virtual image and the image is behind the mirror.
We have, from the given data, u=30 cm and v =−10 cm.
⇒1f=130−110=−115.
⇒f=−15 cm.
If the distance of the object from the mirror is doubled, we get, u=60 cm.
Then, we have, 1v=1f−1u
⇒1v=−115−160=−112.
⇒v=−12.
Thus, it can be seen that if the distance of the object from the mirror doubled, the image if formed at a distance of 12 cm from the mirror i.e. the distance of the image from the mirror increases by 20%,
First, the generalized curved mirror equation:
(1 / u) + (1 / v) = (1 / f) = (2 / r).
u: object distance
v: image distance
f: focal length
r: radius of curvature of the reflecting surface
Now, the sign convention and general assumptions:
I) Aperture of the curved surface mirror is small.
II) All distances are measured from the pole of the mirror.
III) All distances measured from the pole to the front of the mirror is negative.
IV) All distances measured from the pole to the back of the mirror is positive.
V) Focal length and radius of curvature of any convex mirror is always positive.
VI) Focal length and radius of curvature of any concave mirror is always negative.
So, object distance is always negative. In the first case, u = (-30) cm and f must be positive. So, the sign of v has to be positive, v = (+10) cm.
{1 / (-30)} + (1 / 10) = (1 / f)
(1 / f) = {(3 - 1) / 30} = (1 / 15)
f = (+ 15) cm.
Now, come to the second case; where u = (-60) cm.
So, {1 / (-60)} + (1 / v) = (1 / 15)
(1 / v) = (1 / 15) + (1 / 60) = (5 / 60) = (1 / 12)
v = (+ 12) cm.
So, the image will be formed 12cm behind the mirror. The image will be real and inverted (since v is positive).
Explanation:
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