Related Problems with Solution
Problem 2 : Lens Formula and Image Formation
Problem Statement: A concave lens with a focal length ((f)) of 10 cm. is placed in front of an object 20 cm. away from it. Determine the position and nature of the image formed by the lens.
Solution :
- Step 1: Given values: $$(f = -10 , \text{cm}), (u = -20 , \text{cm})$$ (negative because it’s in the direction of the incident light).
- Step 2: Use the lens formula: $$(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}) to find (v).$$
- Step 3: Substitute the values: $$(\frac{1}{-10} = \frac{1}{v} - \frac{1}{-20}).$$
- Step 4: Solve for $$(v): (v = -6.67 , \text{cm}).$$
- Step 5: Analyze the result:
- Since (v) is negative, the image is formed on the same side as the object, which is a virtual image.
- The negative value of (v) indicates that the image is 6.67 cm to the left of the lens. So, the image is virtual and located 6.67 cm to the left of the lens.
