In the figure, an object is placed in front of a converging lens at a distance equal to twice the focal length f 1 of the lens. On the other side of the lens is a concave mirror of focal length f 2 separated from the lens by a distance 2( f 1 + f 2 ). Light from the object passes rightward through the lens, reflects from the mirror, passes leftward through the lens, and forms a final image of the object. Take f 1 = 3.3 cm and f 2 = 3.0 cm. What are (a) the distance between the lens and the final image and (b) the overall lateral magnification M of the object? Is the image (c) real or virtual (if it is virtual, it requires someone looking through the lens toward the mirror), (d) to the left or right of the lens, and (e) inverted or noninverted relative to the object? fi 2 to 0 212) Solution (a). the distance of object measured from a concave mirror is s2 = 2(f1 + f2) - 2f1 = 2f2 first, the light refract from a concave mirror mirror : 1/s2 + 1/s2\' = 1/f2 1/(2f2) + 1/s2\' = 1/f2 1/s2\' = 1/(2f2) s2\' = 2f2 the distance of image from a converging lens is s1 = 2(f1 + f2) - s2\' = 2(f1 + f2) - 2f2 s1 = 2f1 Let s1\' is the distance of final image from a converging lens. 1/s1 + 1/s1\' = 1/f1 1/(2f1) + 1/s1\' = 1/f1 1/s1\' = 1/(2f1) s1\' = 2f1 = 2(3.3) s1\' = 6.6 cm (b). M = (s1\'/s1)(s2\'/s2) = (2f1/2f1)(2f2/2f2) M = 1 c) real d) left e) as M=1 (+ve) so noninverted .

1. In the figure, an object is placed in front of a converging lens at a distance equal to twice the
focal length f 1 of the lens. On the other side of the lens is a concave mirror of focal length f 2
separated from the lens by a distance 2( f 1 + f 2 ). Light from the object passes rightward through
the lens, reflects from the mirror, passes leftward through the lens, and forms a final image of the
object. Take f 1 = 3.3 cm and f 2 = 3.0 cm. What are (a) the distance between the lens and the final
image and (b) the overall lateral magnification M of the object? Is the image (c) real or virtual (if
it is virtual, it requires someone looking through the lens toward the mirror), (d) to the left or
right of the lens, and (e) inverted or noninverted relative to the object?
fi 2 to 0 212)
Solution
(a).
the distance of object measured from a concave mirror is
s2 = 2(f1 + f2) - 2f1 = 2f2
first, the light refract from a concave mirror mirror :
1/s2 + 1/s2' = 1/f2
1/(2f2) + 1/s2' = 1/f2
1/s2' = 1/(2f2)
s2' = 2f2
the distance of image from a converging lens is
s1 = 2(f1 + f2) - s2' = 2(f1 + f2) - 2f2
s1 = 2f1
Let s1' is the distance of final image from a converging lens.

2. 1/s1 + 1/s1' = 1/f1
1/(2f1) + 1/s1' = 1/f1
1/s1' = 1/(2f1)
s1' = 2f1 = 2(3.3)
s1' = 6.6 cm
(b).
M = (s1'/s1)(s2'/s2) = (2f1/2f1)(2f2/2f2)
M = 1
c) real
d) left
e) as M=1 (+ve) so noninverted