Power of a concave lens is 5D. An object is placed at a distance of 40cm from the lens. Calculate the image distance(with sign).

Sure, let's solve this step by step.

Step 1: Identify the given values. The power of the lens, P = -5D (The power of a concave lens is taken as negative) The object distance, u = -40cm (In lens formula, the object distance is always taken as negative)

Step 2: Use the lens formula to find the image distance. The lens formula is 1/f = 1/v - 1/u

Step 3: Convert the power of the lens to focal length. The power of a lens is the reciprocal of its focal length. So, f = 1/P = 1/(-5) = -0.2m = -20cm

Step 4: Substitute the values into the lens formula. 1/(-20) = 1/v - 1/(-40)

Step 5: Solve the equation for v. 1/v = 1/(-20) + 1/40 = -2/40 + 1/40 = -1/40

So, v = -40cm

The negative sign indicates that the image is formed on the same side as the object, which is a characteristic of virtual images formed by concave lenses.