An object is placed at a distance of 40 cm from a convex lens of focal length 20

An object is placed at a distance of 40 cm from a convex lens of focal length 20 cm. Where will the image be formed?

An object is placed at a distance of 40 cm from a convex lens of focal length 20 cm. Where will the image be formed?

Step 1: Identify the given values. The object distance (u) is -40 cm (negative because it is on the same side as the object) and the focal length (f) is +20 cm (positive for a convex lens).
Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
Step 3: Substitute the known values into the lens formula: 1/20 = 1/v - 1/(-40).
Step 4: Simplify the equation: 1/20 = 1/v + 1/40.
Step 5: Find a common denominator for the right side. The common denominator for 20 and 40 is 40.
Step 6: Rewrite the equation: 1/20 = 1/v + 1/40 becomes 1/20 = 2/40 + 1/40.
Step 7: Combine the fractions on the right side: 1/20 = 3/40.
Step 8: Cross-multiply to solve for v: 3 * 20 = 1 * 40v, which gives 60 = 40v.
Step 9: Divide both sides by 40 to find v: v = 60/40 = 1.5 cm.
Step 10: Therefore, the image is formed at a distance of 10 cm on the opposite side of the lens.

Lens Formula – The lens formula relates the focal length (f), the object distance (u), and the image distance (v) for lenses, given by 1/f = 1/v - 1/u.
Convex Lens Properties – A convex lens converges light rays and can form real or virtual images depending on the position of the object relative to the focal length.