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 60 cm from the lens, what is the distance of the image from the lens?
15 cm
30 cm
45 cm
60 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 60 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 -60 cm (we use a negative sign for object distance in lens formula).
Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
Step 3: Substitute the known values into the lens formula: 1/20 = 1/v - 1/(-60).
Step 4: Simplify the equation: 1/20 = 1/v + 1/60.
Step 5: Find a common denominator for the right side of the equation. The common denominator for 20 and 60 is 60. Rewrite the equation: 1/20 = 3/60 + 1/v.
Step 7: Rearrange the equation to isolate 1/v: 1/v = 3/60 - 1/20.
Step 8: Convert 1/20 to have a denominator of 60: 1/20 = 3/60. Now the equation is: 1/v = 3/60 - 3/60.
Step 9: Calculate 1/v: 1/v = 0.05 - 0.05 = 0. This means v = 30 cm.
Step 10: The distance of the image from the lens is 30 cm.
Lens Formula – The lens formula relates the focal length (f), the object distance (u), and the image distance (v) in a lens system, expressed as 1/f = 1/v - 1/u.
Convex Lens Properties – A convex lens converges light rays and can produce real and virtual images depending on the position of the object relative to the focal length.
