Related Problems with Solution

Problem 1 : Lens Image Formation#

Problem Statement: A converging lens with a focal length of 20 cm is placed 30 cm away from an object. Determine the position and nature of the image formed by the lens.

Solution :#

• Step 1: Given values: $$(f = 20 , \text{cm}), (u = -30 , \text{cm})$$ (negative because it’s in the direction of the incident light).
• Use the lens formula: $$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$ to find $v$.
• Step 3: Substitute the values: $$(\frac{1}{20} = \frac{1}{v} + \frac{1}{30}).$$
• Step 4: Solve for $v$: $v = 60\ \text{cm}$
• Step 5: Analyze the result:
  • Since (v) is positive, the image is formed on the same side as the object, which is the real image.
  • The positive value of (v) indicates that the image is 60 cm to the right of the lens.

So, the image is real and located at 60 cm to the right of the lens.