An object is placed 30 cm in front of a convex lens of focal length 15 cm. What

An object is placed 30 cm in front of a convex lens of focal length 15 cm. What is the image distance?

An object is placed 30 cm in front of a convex lens of focal length 15 cm. What is the image distance?

Step 1: Identify the given values. The object distance (u) is 30 cm and the focal length (f) of the convex lens is 15 cm.
Step 2: Use the lens formula, which is 1/f = 1/v - 1/u.
Step 3: Substitute the values into the lens formula. Since the object distance (u) is in front of the lens, we take it as negative: u = -30 cm.
Step 4: Substitute f = 15 cm and u = -30 cm into the formula: 1/15 = 1/v - 1/(-30).
Step 5: Simplify the equation: 1/15 = 1/v + 1/30.
Step 6: Find a common denominator for the right side of the equation, which is 30v: 1/15 = (2 + v)/(30v).
Step 7: Cross-multiply to solve for v: 30v/15 = 2 + v.
Step 8: Simplify the equation: 2v = 2 + v.
Step 9: Isolate v: 2v - v = 2, so v = 2 cm.
Step 10: The image distance (v) is 10 cm.

Lens Formula – The lens formula relates the focal length (f), object distance (u), and image distance (v) of a lens, expressed as 1/f = 1/v - 1/u.
Sign Convention – Understanding the sign convention for lenses is crucial, where object distance (u) is negative for real objects placed in front of the lens.
Convex Lens Properties – A convex lens converges light rays and can produce real or virtual images depending on the object distance relative to the focal length.