Answer to Question #248741 in Optics for Sam

Question

Two thin, long lenses are separated by 20 mm from each other. An object of height 21 mm is placed at 30 mm in front (to the left) of the first lens and the entire system is suspended in air. The first lens has an optical power of +50 D. The second lens is a biconvex lens of radii of curvature of 25 mm and 100 mm. Both lenses have a refractive index of 1.5.

a.     Describe the intermediate and resulting final image of this two-lens system.

b. With the aid of ray diagram, sketch how the intermediate and final images are formed. Indicate all relevant object and image distances and focal lengths on this sketch.   

Answer 1

$\frac 1{F_2}=(n-1)(\frac 1{R_1}+\frac 1{R_2})=\frac 1{0.04},$

$F_1=0.02~m,~F_2=0.04~m,$

$\frac 1F=\frac 1{F_1}+\frac1{F_2}-\frac L{F_1 F_2}=\frac 1{0.02},$

$F=0.02~m,$

$f=\frac {dF}{d-F}=0.06~m,$

$\Gamma=\frac Hh=\frac fd=2,$

$H=2h=42~mm.$