An object is placed 25 cm from a convex lens of focal length 10 cm. Where is the

An object is placed 25 cm from a convex lens of focal length 10 cm. Where is the image formed?

An object is placed 25 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 -25 cm (negative because it is on the same side as the incoming light) 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/(-25).
Step 4: Simplify the equation: 1/10 = 1/v + 1/25.
Step 5: Find a common denominator for the right side. The common denominator for 10 and 25 is 50.
Step 6: Rewrite the equation: 1/10 = 5/50 + 2/50, which simplifies to 1/10 = 7/50.
Step 7: Rearrange the equation to solve for 1/v: 1/v = 1/10 - 7/50.
Step 8: Convert 1/10 to have a denominator of 50: 1/10 = 5/50.
Step 9: Now, calculate: 1/v = 5/50 - 7/50 = -2/50.
Step 10: Invert the fraction to find v: v = -25/2 = -12.5 cm.
Step 11: Since v is negative, it indicates that the image is formed on the same side as the object.

Lens Formula – The lens formula relates the focal length (f), object distance (u), and 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.