Find the location and height of the child\'s image for light which first reflect

Question

Find the location and height of the child's image for light which first reflects off of the mirror and then passes through the lens. Determine your solution graphically as well. Use f(mirror)=fM=2m and f(lens)=fL=4m. The center of the lens and the mirror are 5m apart and the child is 0.8m tall. The child is 2.5m from the mirror.

The picture is :

Find the location and height of the child's image for light which first reflects off of the mirror and then passes through the lens. Determine your solution graphically as well. Use f(mirror)=fM=2m and f(lens)=fL=4m. The center of the lens and the mirror are 5m apart and the child is 0.8m tall. The child is 2.5m from the mirror. The picture is :

Explanation / Answer

for mirror

(1/S1) + (1/S1') = 1/f

1/2.5 + 1/S1' =1/2

S1' = 10 m

the first image produced by the mirror is 10 m to the left of the lens . this acts as virtual object to the lens
. so the object distance is taken as -ve
for lens
distance bwetween len and mirror

d = 5 m

S2 =10-5 = 5 m

(1/S2)+(1/S2') =1/F

(-1/ 5) + (1/S2') =(1/4)

S2' = 2.22 m to the left of the lens

magnitude of magnification for mirror m1 = S1'/S1 = 10/2.5 = 4

for lens m2 = S2'/S2 = 2.22/5= 0.444

total magnification M = m1*m2 =4*0.444

M = Image / object height

Image height = 4*0.444*0.8 = 1.42 m

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