If a lens forms a real image at a distance of 40 cm from the lens, and the objec

If a lens forms a real image at a distance of 40 cm from the lens, and the object is placed at 60 cm, what is the focal length of the lens?

If a lens forms a real image at a distance of 40 cm from the lens, and the object is placed at 60 cm, what is the focal length of the lens?

Step 1: Identify the given values. The image distance (v) is 40 cm and the object distance (u) is -60 cm (negative because the object is on the same side as the incoming light).
Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
Step 3: Substitute the values into the lens formula: 1/f = 1/40 - 1/(-60).
Step 4: Simplify the equation: 1/f = 1/40 + 1/60.
Step 5: Find a common denominator to add the fractions. The common denominator of 40 and 60 is 120.
Step 6: Convert the fractions: 1/40 = 3/120 and 1/60 = 2/120.
Step 7: Add the fractions: 1/f = 3/120 + 2/120 = 5/120.
Step 8: Simplify the fraction: 1/f = 1/24.
Step 9: Take the reciprocal to find the focal length: f = 24 cm.

Lens Formula – The lens formula relates the focal length (f), the image distance (v), and the object distance (u) through the equation 1/f = 1/v - 1/u.
Sign Convention – Understanding the sign convention for distances is crucial; object distance (u) is negative for real objects placed on the same side as the incoming light.
Real and Virtual Images – Recognizing the difference between real and virtual images, where real images are formed on the opposite side of the lens from the object.