Assertion:- If an object placed on the optic axis of a lens is illuminated by white light, then image formed will be coloured and not exactl white.
Reason:- The lens has different focal length sfor different colours.

Options

A. If both Assertion `&` Reason are True `&` the Reason is a correct explanation of the Assertion.
B. If both Assertion `&` Reason are True but Reason is not a correct explanation of the Assertion.
C. If Assertion is True but the Reason is False.
D. If both Assertion `&` Reason are False.

Answer

To solve the assertion and reason question, we need to analyze both the assertion and the reason provided:

**Assertion:** If an object placed on the optic axis of a lens is illuminated by white light, then the image formed will be colored and not exactly white.

**Reason:** The lens has different focal lengths for different colors.

### Step-by-Step Solution:

1. **Understanding White Light and Lenses:**
- White light is composed of multiple colors (spectrum) such as red, orange, yellow, green, blue, indigo, and violet.
- When white light passes through a lens, it can be refracted (bent) differently depending on the wavelength (color) of the light.

2. **Refraction in Lenses:**
- Lenses have a property called dispersion, which means they can bend different colors of light by different amounts.
- For example, shorter wavelengths (like blue) are bent more than longer wavelengths (like red).

3. **Different Focal Lengths:**
- Because of this difference in bending, each color of light will focus at a slightly different point. This means that if you have white light passing through a lens, the different colors will not converge at the same point.
- This leads to the formation of a colored image rather than a white image, as the colors are spread out.

4. **Conclusion on Assertion:**
- Therefore, the assertion is true: when white light is passed through a lens, the image formed will indeed be colored due to the different focal lengths for different colors.

5. **Conclusion on Reason:**
- The reason is also true: the lens does have different focal lengths for different colors due to the phenomenon of dispersion.

6. **Relationship between Assertion and Reason:**
- The reason explains why the assertion is true. The different focal lengths for different colors directly lead to the formation of a colored image when white light is used.

### Final Answer:
- Both the assertion and the reason are true, and the reason provides a correct explanation for the assertion.

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