An object is placed at a distance of 15 cm from a convex lens of focal length 10

An object is placed at a distance of 15 cm from a convex lens of focal length 10 cm. Where is the image formed?

An object is placed at a distance of 15 cm from a convex lens of focal length 10 cm. Where is the image formed?

Step 1: Identify the given values. The object distance (u) is -15 cm (negative because it is on the same side as the object) and the focal length (f) is +10 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: 1/10 = 1/v - 1/(-15).
Step 4: Simplify the equation: 1/10 = 1/v + 1/15.
Step 5: Find a common denominator for the right side, which is 30. Rewrite the equation: 1/10 = 1/v + 2/30.
Step 6: Convert 1/10 to have a denominator of 30: 3/30 = 1/v + 2/30.
Step 7: Rearrange the equation: 3/30 - 2/30 = 1/v, which simplifies to 1/30 = 1/v.
Step 8: Take the reciprocal to find v: v = 30 cm.
Step 9: Interpret the result: The image is formed 30 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) of a lens, expressed as 1/f = 1/v - 1/u.
Convex Lens Properties – A convex lens converges light rays and can form real and virtual images depending on the position of the object relative to the focal length.
Sign Convention – Understanding the sign convention for distances in optics is crucial, where object distance is negative for real objects placed on the same side as the incoming light.