Question

An object is placed 20 cm from a converging lens with focal length 15 cm. A concave mirror with focal length 10 cm is located 75 cm to the right of the lens asshown in the figure. Note: The figure is not drawn to scale. A)

Determine the location of the final image.

B)

If the height of the object is 1.0 cm, what is the height of the image?

thanks!

Answer 1

Given dataInitial object distance, p₁ = 20 cmFocal length of the converging lens, f₁= 15 cmFocal length of the concave mirror, f₂= 10 cmDistance between the two lenses is, d = 75 cmHeight of the object is, h_o = 1.0 cmSolution:(A)The image distance for the converging lens can becalculated by using thin lens equation1/f₁ = 1/p₁ + 1/q₁1/q₁ = 1/ 20 cm - 1/ 15 cmq₁ = - 60 cm-------------------------------------------------------------------------------This image is the object for the mirror, and the object distance for theconverging mirror is,p₂=d-q₁= 75 cm - (-60 cm)= 135 cmThe image distance for the convergingmirror is,1/f₂ = 1/p₂ + 1/q₂1/q₂ = 1/10 cm - 1/135 cmq₂ = 10.8cmThe final image is 10.8 cm to the right of the converging mirror---------------------------------------------------------------------------------(B) Magnification for the converging lens is,m₁ =-q₁ / p₁= -(-60 cm) / 15 cm= 4Magnification for the convergingmirror is,m₂= -q₂ /p_{2= -10.8 cm / (135 cm)= -0.08Overall Magnification,M = m1m2}= 4 * 0.08= 0.32Since , M = h_i / h_o0.32 = h_i / 1.0 cmh_i = 0.32 cmThe height of the image is 0.32 cm