If the magnification of a virtual image formed by an object 10cm from a convex less is 3, then the focal length of the lens is

Answer Details

To find the focal length of a convex lens, we can use the formula: 1/f = 1/do + 1/di where f is the focal length of the lens, do is the distance of the object from the lens, and di is the distance of the image from the lens. In this case, the image is virtual and the magnification is given as 3. This means that the image is 3 times larger than the object. We can use the magnification formula to find the distance of the image from the lens: m = -di/do where m is the magnification, di is the distance of the image from the lens, and do is the distance of the object from the lens. Substituting m = 3 and do = 10cm, we get: 3 = -di/10cm Solving for di, we get: di = -30cm Note that the negative sign indicates that the image is virtual. Now we can use the lens formula to find the focal length of the lens: 1/f = 1/do + 1/di Substituting do = 10cm and di = -30cm, we get: 1/f = 1/10cm + 1/-30cm Simplifying the equation, we get: 1/f = -1/15cm Multiplying both sides by -15cm, we get: f = -15cm Note that the negative sign indicates that the lens is a convex lens. Therefore, the focal length of the lens is -15cm or 15cm (taking the absolute value). Option D, 15cm, is the correct answer.