An object is placed in front of a concave and convex mirror as shown below. Determine the value of 'x' if the virtual images are formed on the same plane. The focal length of the concave and convex mirrors are 40 cm and 6.5 cm, respectively.
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An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is 30 cm, it is found that that is no parallax between the images formed by the two mirrors. What is the radius of curvature of the convex mirror?
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A
25cm
As shown in figure, the plane mirror will form erect and virtual image of same size at a distance of 30 cm behind it. So, the distance of image formed by plane mirror from convex mirror will be
PI=MI−MP
But as, MI=MO
PI=MO−MP=30−20=10 cm
Now, as this image coincides with the image formed by convex mirror, therefore for convex mirror,
u=−50 cm;v=+10 cm
So,
+10
1
+
−50
1
=
f
1
, i.e., f=
4
50
=12.5 cm
So, R=2f=2×12.5=25 cm.
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