Question

 A pencil of height 1 cm is placed 30 cm from an equviconvex lens, refractive index n =3/2, radius of curvature for both the surfaces, R₁ = R₂ = R = 10 cm. Find the location of the image and describe its characteristics.  

Answer 1

 The ray of light diverges from the object; it is a real object. Focal length of a convex lens is positive. 

(1/f) =[(n₂-n₁)/n₁](2/R) = [(3/2) -1]/1(2/10) = 1/10 

The given parameters are 

u = -30 cm 

f= +10 cm 

substituting these values in thin lens equation, we have (1/v) – (1/u) = (1/f) 

(1/v) – (1/-30) = (1/10) 

which on solving gives v = +15 cm. 

The image distance is positive, which implies that the image is real. The lateral magnification is

m = v/u = 15/(-30) = -1/2 

The image is half the size of the object; size of the image is 0.50 cm. 

The negative sign with magnification shows inverted image.