A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is (a) a convex lens of a focal length 20 cm, and (b) a concave lens of focal length 16 cm?
Here, the point P on the right of the lens acts as a virtual object. Object distance, u = 12 cm Focal length, f = 20 cm (a) Using the lens formula, 1v =1f+1u∴ 1v =120+112 =3+560 =860 i.e., v = 60/8 = 7.5 cm. Image is at a distance of 7.5 cm to the right of the lens, where the beam converges. (b)Now,Focal length of concave lens, f = –16 cmObject distance, u = 12 cm ∴ 1v=1f+1u =-116+112 = -3+448 =148 ⇒ v = 48 cm Hence, the image is at a distance of 48 cm to the right of the lens, where the beam would converge. |