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 position of the image formed? (2020)

An object is placed 30 cm in front of a convex lens of focal length 15 cm. What is the position of the image formed? (2020)

Step 1: Identify the given values. The object distance (u) is -30 cm (negative because it is in front of the lens) and the focal length (f) is 15 cm.
Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
Step 3: Substitute the known values into the lens formula: 1/15 = 1/v - 1/(-30).
Step 4: Simplify the equation: 1/15 = 1/v + 1/30.
Step 5: Find a common denominator for the right side of the equation, which is 30v: 1/15 = (2 + v)/(30v).
Step 6: Cross-multiply to solve for v: 30v/15 = 2 + v.
Step 7: Simplify the equation: 2v = 2 + v.
Step 8: Isolate v: 2v - v = 2, so v = 2 cm.
Step 9: The position of the image formed is 10 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 lenses, expressed as 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.
Sign Convention – Understanding the sign convention for distances in optics, where object distance (u) is negative for real objects placed in front of the lens.