At an intersection of hospital hallways, a convex mirror is mounted high on a wall to help people avoid collisions. The mirror has a radius of curvature of 0.550 m. Where will the image of a patient 10.0 m from the mirror be located? (Assume that the patient is along the principal axis of the mirror, and that the paraxial approximation holds.)
At an intersection of hospital hallways, a convex mirror is mounted high on a wall to help people avoid collisions. The mirror has a radius of curvature of 0.550 m. Where will the image of a patient 10.0 m from the mirror be located? (Assume that the patient is along the principal axis of the mirror, and that the paraxial approximation holds.)
The correct option is D 26.7 cm, behind the mirror.
We have,
f=+0.275m(recall,f=R2),u=−10m (Quick recap: according to sign convention, distances measured along direction of incident ray are taken as positive, and the reverse as negative. As a result of this, a concave mirror always has negative focal length, and convex mirror positive)
Using mirror formula,
1u+1v=1fOr,1v=1f−1u.Substituting the values;1v=10.275−1−10=10+0.2752.75We get,1v=3.74m−1.
Hence,
v=+26.7 cm or 26.7 cm ,in beind the mirror, or opposite to the side of the object (A positive value of v means image lies behind the mirror).
Note a couple of things: a convex mirror always forms a image behind it, between pole and focus. If, your answer for any problem of convex mirrors comes out beyond the limits, you are sure it is wrong, you go back, check sign convention, calculations etc and thank me!)
We have,
f=+0.275m(recall,f=R2),u=−10m
(Quick recap: according to sign convention, distances measured along direction of incident ray are taken as positive, and the reverse as negative. As a result of this, a concave mirror always has negative focal length, and convex mirror positive)
Using mirror formula,
1u+1v=1fOr,1v=1f−1u.Substituting the values;1v=10.275−1−10=10+0.2752.75We get,1v=3.74m−1.
Hence,
v=+26.7 cm or 26.7 cm ,in beind the mirror, or opposite to the side of the object (A positive value of v means image lies behind the mirror).
Note a couple of things: a convex mirror always forms a image behind it, between pole and focus. If, your answer for any problem of convex mirrors comes out beyond the limits, you are sure it is wrong, you go back, check sign convention, calculations etc and thank me!)
