A lens forms a real image at a distance of 30 cm from the lens when the object i

A lens forms a real image at a distance of 30 cm from the lens when the object is placed at 10 cm. What is the focal length of the lens?

A lens forms a real image at a distance of 30 cm from the lens when the object is placed at 10 cm. What is the focal length of the lens?

Step 1: Identify the given values. The distance of the image (v) is 30 cm, and the distance of the object (u) is -10 cm (we use a negative sign for the object distance in lens formulas).
Step 2: Write down the lens formula: 1/f = 1/v + 1/u.
Step 3: Substitute the values into the lens formula: 1/f = 1/30 + 1/(-10).
Step 4: Calculate 1/(-10): it equals -0.1.
Step 5: Now, calculate 1/f: 1/f = 1/30 - 0.1.
Step 6: Convert 1/30 to a decimal: 1/30 = 0.0333.
Step 7: Now, combine the values: 1/f = 0.0333 - 0.1 = -0.0667.
Step 8: To find f, take the reciprocal: f = 1/(-0.0667).
Step 9: Calculate the focal length: f = -15 cm. Since we need the absolute value, the focal length is 5 cm.

Lens Formula – The lens formula relates the focal length (f), object distance (u), and image distance (v) of a lens, given by 1/f = 1/v + 1/u.
Real and Virtual Images – Understanding the difference between real and virtual images is crucial, as real images are formed on the opposite side of the lens from the object.
Sign Convention – Applying the correct sign convention for distances (positive for real and negative for virtual) is essential for accurate calculations.