A beam of light passes through a thin convex lens with a focal length of 15 cm.
Practice Questions
Q1
A beam of light passes through a thin convex lens with a focal length of 15 cm. If the object is placed 30 cm from the lens, what is the image distance?
10 cm
15 cm
20 cm
30 cm
Questions & Step-by-Step Solutions
A beam of light passes through a thin convex lens with a focal length of 15 cm. If the object is placed 30 cm from the lens, what is the image distance?
Step 1: Identify the given values. The focal length (f) of the lens is 15 cm, and the object distance (u) is 30 cm.
Step 2: Remember that in lens formulas, the object distance (u) is taken as negative. So, u = -30 cm.
Step 3: Write down the lens formula: 1/f = 1/v - 1/u.
Step 4: Substitute the known values into the lens formula: 1/15 = 1/v - 1/(-30).
Step 5: Simplify the equation: 1/15 = 1/v + 1/30.
Step 6: To combine the fractions on the right side, find a common denominator. The common denominator for 15 and 30 is 30.
Step 7: Rewrite 1/15 as 2/30. Now the equation looks like: 2/30 = 1/v + 1/30.
Step 8: Subtract 1/30 from both sides: 2/30 - 1/30 = 1/v.
Step 9: This simplifies to 1/30 = 1/v.
Step 10: Invert both sides to find v: v = 30 cm.
Lens Formula – The relationship between the focal length (f), object distance (u), and image distance (v) in lens systems, expressed as 1/f = 1/v - 1/u.
Sign Convention – Understanding the sign conventions for object distance (u) and image distance (v) in optics, where distances measured against the direction of incident light are negative.
