A 10.0 cm tall pencil is placed upright in the region between a concave mirror a

Question

A 10.0 cm tall pencil is placed upright in the region between a concave mirror and a c mirror (concave and convex relative to the pencil at its location). The concave mirror has a radius curvature of JR1 f= 12.0 cm. whereas the convex mirror has the radius of curvature of |R2|- 10.0 cm. mirrors are thin, and their vertices are distance 30.0 cm apart. The pencil is located 10.0 cm away from t c vertex of the concave mirror. Find the location of the final image. Is it real or imaginary, erect or inverted? Also, find the overall magnification. Start with an accurate sketch of this scenario (make sure it is quantitatively correct)! First, find the image obtained after the light from the pencil reflects off of the concave mirror; then, use the image crated in this reflection as the object for the convex mirror. Final magnification is: (location of the final image)/(very initial location of the object), but this equals to the product of the magnification of the first and the magnification of the second mirror!

Explanation / Answer

For reflection from concave mirror

=>    1/v = 1/6 - 1/10

=> v =   15 cm

=> magnification , m1 = -v/u = -15/10 = - 1.5

=>   first image is real inverted and enlarged .

For reflection from convex mirror

=>   1/v = -1/5   - 1/15

=> v =   - 3.75 cm

=>    magnification , m2 = 3.75/15 = 0.25

=>    Final magnification = m1 * m2

                                         = - 1.5 * 0.25 = - 0.375

=> Final image is virtual , inverted with respect to original object .

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