Question

A biconvex lens, f₁ = 20 cm, is placed 5 cm infront of a convex mirror, f₂ = 15 cm, an object of length 2 cm is placed at a distance 10 cm from the lens. Find the location of three images: 

(a) the image formed by the lens as the rays travel to the right, 

(b) the image formed after the rays reflect from the mirror and 

(c) the final image after the leftward travelling rays once again pass through the lens.  

Answer 1

(a) From lens equation, (1/v) – (1/-10) = -(1/20) , v = -20 cm 

magnification m1 = (-20)/(-10) = +2 

image is virtual, erect and magnified. 

(b) the first image acts as an object for the convex mirror. Object distance for the mirror, 

u’ = (20+5) = 25 cm. 

From mirror equation, (1/v’) + (1/-25) = (1/15) 

v’ = +75/8 cm 

magnification, m₂ = (+75/8)/(-25) = 3/8 

image is virtual (to the right of the mirror), erect and diminished. 

(c) the object distance for second refraction at the lens = (75/8) +5 = 115/8 

From lens equation, (1/v’’) – 1/(+115/8) = 1/-20 

v’’= 460/9 = +51.1 cm 

magnification m₃ = (+460/9)/(115/8) = 32/9 

overall magnification m = m₁*m₂*m₃ = 2(3/8)(32/9) = 8/3 

hence size of image=(8/3)2 cm= 5.33 cm 

Final image is to the right of the lens at a distance 51.1 cm from the lens, real, erect and magnified.