A lens forms a real image of a height 5 cm at a distance of 40 cm from the lens.
Practice Questions
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
Questions & Step-by-Step Solutions
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?
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.
Magnification – The ratio of the height of the image to the height of the object, which is also related to the distances of the object and image from the lens.
Lens Formula – Understanding the relationship between object distance (u), image distance (v), and focal length of the lens.
