a concave mirror of focal length `20 cm` and a convex mirror of focal length `15 cm` are placed `50 cm` apart, such that the two mirrors face eaachother. An object is placed exactly midway between them. Fing the nature and position of image formed by reflection first at concave mirror and then at convex mirror.

Explanation

Here, `f_1 = - 20 cm, f_2 = 15 cm`
`u_1 = -(50)/(2) cm = -25 cm`
(i) Formation of image by concave mirror `M_1`
`(1)/(v_1)=(1)/(f_1)-(1)/(u_1) = (1)/(-20)-(1)/(-25) = (-1)/(100)`
`v_1 = -100 cm`
As `v_1` is negative, image of object `AB` is real and inverted, formed in front of concave mirror at
`A' B'`, where `P_1 B' = 100 cm`, Fig..
(ii) Formation of image by convex mirror `M_2`
The real image `A'B'` acts as virtual object for concave mirror.
`:. u_2 = P_2 B' = P_1B' - P_1 P_2 = (100 - 50)`
=`50 cm`
The final image is `A" B"` , where `P_2 B" = v_2`
`(1)/(v_2) = (1)/(f_2) - (1)/(u_2) = (1)/(15) - (1)/(50) = (7)/(150)`
`v_2 = (150)/(7) = 21.43 cm`.
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