The magnification produced by a concave lens of power P is 1/2 for an object placed at a distance of 20cm from it. Calculate P.

The magnification (m) of a lens is given by the formula m = -v/u, where v is the image distance and u is the object distance.

Given that m = 1/2 and u = -20 cm (the negative sign indicates that the object is on the same side of the lens as the light being used), we can substitute these values into the formula to find v:

1/2 = -v/-20

Solving for v gives v = -10 cm.

The power (P) of a lens is given by the formula P = 1/f, where f is the focal length of the lens. The lens formula, which relates the object distance (u), the image distance (v), and the focal length (f), is given by 1/f = 1/v - 1/u.

Substituting the given values of v = -10 cm and u = -20 cm into the lens formula gives:

1/f = 1/-10 - 1/-20

Solving for f gives f = -20 cm.

Finally, substituting f = -20 cm into the formula for P gives P = 1/-20 = -0.05 D.

Therefore, the power of the lens is -0.05 D.