A concave mirror and a convex mirror of focal lengths 10cm and 15cm are places at a distance of 70cm. An object AB of height 2cm is places at a distance of 30cm from the concave mirror. First ray is incident on the concave mirror then on the convex mirror. Find size, position, and nature of the image.

Explanation

For concave mirror,
u=-30cm, f=-10cm
Using `1/v+1/u=1/f rArr1/v=1/(30)=(-1)/(10)rArr v=-15cm`
Now, `(A^(')B^('))/
(AB)=(-v)/u=((-15))/((-30))rArrA^(')B^(')=-1cm`
Image formed by first reflection will be real, inverted , and diminished.
For convex mirror, the image formed by concave mirror will act as object for convex mirror. Now object distance for convex mirror
`O_2A^(')=70-15`
`=55cm`
`u^(')=-55cm,f^(')`
`=+15cm`
Using `1/(v^(')) +1/(u^')=1/(f^('))`
`rArr1/v^(')-1/(55)=1/(15)`
`rArrv^(')=(165)/(14) cm`
Now, `(A^('')B^(''))/(A^(')B^('))=-v^(')/u^(')=-((+165/14))/((-55))`
`rArr A^('')B^('') =(-3/(14))(-1)=-0.2cm`
Final image will be virtual, inverted, and diminished.
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