A lens forms a real image at a distance of 40 cm from the lens when the object i

A lens forms a real image at a distance of 40 cm from the lens when the object is placed at 20 cm. What is the focal length of the lens?

A lens forms a real image at a distance of 40 cm from the lens when the object is placed at 20 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 20 cm.
Step 2: Remember that in lens formulas, the object distance (u) is taken as negative. So, u = -20 cm.
Step 3: Write down the lens formula: 1/f = 1/v - 1/u.
Step 4: Substitute the values into the formula: 1/f = 1/40 - 1/(-20).
Step 5: Calculate 1/40, which is 0.025, and 1/(-20), which is -0.05.
Step 6: Now, calculate 1/f = 0.025 + 0.05.
Step 7: Add the two values: 1/f = 0.025 + 0.05 = 0.075.
Step 8: To find f, take the reciprocal: f = 1/0.075.
Step 9: Calculate f, which gives you f = 13.33 cm (approximately).

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 lenses is crucial, where 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.