Answer:
According to the question, we are given that,
Distance of the tooth from the mirror or object distance, u=−2.2 cmu=−2.2 cm, the negative sign implies that the measurements are taken from the pole and against the direction of the incident light.
Magnification, m=4.5m=4.5 positive value of magnification implies that the image is upright, and magnification greater than 1 implies that the image is magnified.
We are required to find the radius of curvature of the mirror. We know that the radius of curvature, R=2fR=2f. Hence we can find the focal length of the mirror, using the mirror formula. But first, let us find the image distance using the magnification formula. i.e.
m=−vuv=−mu=−4.5×(−2.2) cmv=9.9 cmm=−vuv=−mu=−4.5×(−2.2) cmv=9.9 cm
The positive value of image distance implies that the image is virtual, as the distance is calculated from the pole and towards the direction of incident light.
Now using the values of object and image distance, let us find the focal length of the mirror.
1f=1v+1u1f=19.9−12.2f≈−2.82 cm1f=1v+1u1f=19.9−12.2f≈−2.82 cm
The negative sign in the focal length implies that the mirror used is a concave mirror or a converging mirror.
Therefore the radius of curvature of the mirror will be,
R=2fR=2×(−2.82)R≈−5.65 cmR=2fR=2×(−2.82)R≈−5.65 cm
Now let us draw the ray diagram for the mirror.
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