An object is placed 50 cm from a converging lens of focal length 25 cm. Where wi

An object is placed 50 cm from a converging lens of focal length 25 cm. Where will the image be formed?

An object is placed 50 cm from a converging lens of focal length 25 cm. Where will the image be formed?

Step 1: Identify the given values. The object distance (u) is -50 cm (negative because it is on the same side as the object) and the focal length (f) is +25 cm (positive for a converging lens).
Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
Step 3: Substitute the known values into the lens formula: 1/25 = 1/v - 1/(-50).
Step 4: Simplify the equation: 1/25 = 1/v + 1/50.
Step 5: Find a common denominator for the right side of the equation, which is 50v: 1/25 = (2 + v)/(50v).
Step 6: Cross-multiply to eliminate the fraction: 50v/25 = 2 + v.
Step 7: Simplify the left side: 2v = 2 + v.
Step 8: Solve for v by isolating it: 2v - v = 2, so v = 2 cm.
Step 9: The image distance (v) is 33.33 cm, which means the image is formed 33.33 cm on the opposite side of the lens.

Lens Formula – The lens formula relates the focal length (f), object distance (u), and image distance (v) for a lens, given by 1/f = 1/v - 1/u.
Converging Lens – A converging lens brings parallel rays of light to a focus, and the image formed can be real or virtual depending on the object distance.
Image Formation – Understanding where the image is formed based on the object distance and focal length is crucial for solving lens problems.