A lens forms a real image of a height 5 cm at a distance of 40 cm from the lens. If the object is placed at 20 cm from the lens, what is the height of the object?
Practice Questions
1 question
Q1
A lens forms a real image of a height 5 cm at a distance of 40 cm from the lens. If the object is placed at 20 cm from the lens, what is the height of the object?
2.5 cm
5 cm
10 cm
20 cm
Using the magnification formula, m = h'/h = -v/u. Here, h' = 5 cm, v = 40 cm, u = -20 cm. Thus, h = (h' * u) / v = (5 * -20) / 40 = 2.5 cm.
Questions & Step-by-step Solutions
1 item
Q
Q: A lens forms a real image of a height 5 cm at a distance of 40 cm from the lens. If the object is placed at 20 cm from the lens, what is the height of the object?
Solution: Using the magnification formula, m = h'/h = -v/u. Here, h' = 5 cm, v = 40 cm, u = -20 cm. Thus, h = (h' * u) / v = (5 * -20) / 40 = 2.5 cm.
Steps: 7
Step 1: Identify the given values from the problem. The height of the image (h') is 5 cm, the distance of the image from the lens (v) is 40 cm, and the distance of the object from the lens (u) is 20 cm (but we will use -20 cm because in lens formulas, object distance is taken as negative).
Step 2: Write down the magnification formula: m = h'/h = -v/u.
Step 3: Substitute the known values into the magnification formula. We have h' = 5 cm, v = 40 cm, and u = -20 cm.
Step 4: Rearrange the formula to find the height of the object (h). The formula becomes h = (h' * u) / v.
Step 5: Substitute the values into the rearranged formula: h = (5 * -20) / 40.
Step 6: Calculate the value: h = (-100) / 40 = -2.5 cm.
Step 7: Since height is usually taken as a positive value, the height of the object is 2.5 cm.
