A convex lens has a focal length of 20 cm. If an object is placed at a distance
Practice Questions
Q1
A convex lens has a focal length of 20 cm. If an object is placed at a distance of 40 cm from the lens, what is the distance of the image from the lens?
20 cm
40 cm
60 cm
80 cm
Questions & Step-by-Step Solutions
A convex lens has a focal length of 20 cm. If an object is placed at a distance of 40 cm from the lens, what is the distance of the image from the lens?
Step 1: Identify the given values. The focal length (f) of the lens is 20 cm, and the object distance (u) is 40 cm.
Step 2: Remember that in lens formulas, the object distance (u) is taken as negative. So, u = -40 cm.
Step 3: Write down the lens formula: 1/f = 1/v - 1/u.
Step 4: Substitute the known values into the lens formula: 1/20 = 1/v - 1/(-40).
Step 5: Simplify the equation: 1/20 = 1/v + 1/40.
Step 6: Find a common denominator for the right side. The common denominator for 20 and 40 is 40.
Step 9: Subtract 2/40 from both sides: 0 = 1/v - 2/40.
Step 10: Rearranging gives us 1/v = 2/40, which simplifies to 1/v = 1/20.
Step 11: Take the reciprocal to find v: v = 20 cm.
Step 12: The image is formed at a distance of 20 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.
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.
Image Formation – Determining the position and nature of the image formed by a convex lens based on the object distance and focal length.
