A lens has a focal length of 40 cm. If an object is placed 80 cm from the lens,

A lens has a focal length of 40 cm. If an object is placed 80 cm from the lens, what is the image distance?

A lens has a focal length of 40 cm. If an object is placed 80 cm from the lens, what is the image distance?

Step 1: Identify the given values. The focal length (f) of the lens is 40 cm, and the object distance (u) is 80 cm.
Step 2: Use the lens formula, which is 1/f = 1/v - 1/u, where v is the image distance.
Step 3: Rearrange the formula to find v: 1/v = 1/f + 1/u.
Step 4: Substitute the values into the formula: 1/v = 1/40 + 1/80.
Step 5: Find a common denominator for the fractions. The common denominator for 40 and 80 is 80.
Step 6: Rewrite the fractions: 1/40 = 2/80, so 1/v = 2/80 + 1/80 = 3/80.
Step 7: Invert the fraction to find v: v = 80/3 cm.
Step 8: Calculate 80/3, which is approximately 26.67 cm. This is the image distance.

Lens Formula – The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens: 1/f = 1/v + 1/u.
Sign Convention – Understanding the sign convention for distances in optics is crucial, where object distance is negative for real objects and image distance can be positive or negative depending on the type of image.