As shown in Figure,. And object O is at the position (-10,2) with respect to the origin P. The concave mirror `M_(1)` has radius of curvature 30cm. A plane mirror `M_(2)` is kept at a distance of 40cm in front of the concave mirror. Considering first refletion on the concave mirror `M_(1)` and second on the plane mirror `M_(2)`. Find the coordinates of the second image w.r.t. the origin P.

Answer

Coordinates of `l_(2) w.r.t. P=(-46,-76)`

Explanation

For `M_(1),u=-10,f=-15,h=2`.
Using mirror formula `(1)/(v)+(1)/(u)=(1)/(f)rArr(1)/(v)+(1)/(-10)=(1)/(-15)`
`rArr (1)/(v)=(1)/(10)-(1)/(15)=(3-2)/(30)`
`rArrv=30 cm & (h_(2))/(h_(1))=-(v)/(u)rArrh_(2)=6 cm`
The iamge formed by the plane mirror is at `70` below the principal axis `& 70+6-30=46` of the concave mirror. `therefore` coordinates of `l_(2)w.r.t.P=(-46,-70)`