A convex mirror has a radius of curvature whose magnitude is 49 cm. The mirror i

Question

A convex mirror has a radius of curvature whose magnitude is 49 cm. The mirror is positioned on a horizontal optical bench with its front surface at 0 cm. A 5.0 cm long fluorescent lamp oriented vertically is placed at +98 cm.

A) What is the focal length of the mirror?

B) At what distance from the mirror can we find a sharp image of the lamp?

C) How tall is the image of the lamp?

D) If the convex mirror were replaced by a plane mirror and the lamp moved to 218 cm from the plane mirror, how tall would the image be?

Explanation / Answer

Given that

A convex mirror has a radius of curvature whose magnitude is (R) =49 cm.

Then the focal length of the convex mirror is (f) =-R/2 =-24.5cm

We know that from the mirror equation we get

1/P+1/q =1/f

Then 1/q =1/f-1/p

=1/(-24.5)-1/+98 =-0.0408-0.0102

Then the image distance is (q) =-19.606cm

The image of the lamp is given by

m =h'/h =q/p

then h' =(q/p)*h =(19.606cm/98)*(5cm) =1cm

If the convex mirror were replaced by a plane mirror and the lamp moved to 218 cm from the plane mirror, how tall would the image be given by the same object height =5cm

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