A convex lens has a focal length of 15 cm. When an object AB is kept at x distance from the lens, then the image formed has magnification +3 but when the object is further displaced by y distance away from the lens as shown in the figure then image formed has magnification –3. ThenOne/More correct answer(s)A.Value of x is 7.5 cmB.Value of y is 10 cmC.Value of x is 10 cmD.Value of y is 20 cm

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.

For a convex lens, the magnification is positive when the image is virtual (on the same side of the lens as the object) and negative when the image is real (on the opposite side of the lens as the object).

Given that the focal length (f) of the lens is 15 cm, we can use the lens formula 1/f = 1/v - 1/u to find the object and image distances.

1. When the magnification is +3, the image is virtual and the object distance (u) is negative. Plugging these values into the magnification formula gives us -v/u = 3. Solving for v gives us v = -3u.

2. We can then substitute v = -3u into the lens formula to get 1/15 = 1/(-3u) - 1/u. Solving this equation gives us u = -7.5 cm. Since u is negative, the object is on the same side of the lens as the light source, so the object distance is 7.5 cm. Therefore, the value of x is 7.5 cm (Option A).

3. When the object is further displaced by y distance away from the lens, the magnification becomes -3, meaning the image is now real. Using the same process as above, we find that u = 30 cm. Since the object was initially 7.5 cm from the lens, the additional distance y is 30 cm - 7.5 cm = 22.5 cm. Therefore, the value of y is 22.5 cm, not 10 cm or 20 cm (Options B and D are incorrect).

4. Therefore, the correct answers are A (Value of x is 7.5 cm) and none of the options given for y are correct.