When monochromatic red light is used instead of blue light in a convex lens, its focal length will
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Q: Why does the refractive index change with the color of light?

The refractive index is a measure of how much light slows down in a medium. Different colors (wavelengths) interact differently with the atoms of the material, causing them to slow down by different amounts. This phenomenon is called dispersion and is mathematically modeled by Cauchy's formula.

Q: Does the radius of curvature of the lens change when we change the color of light?

No, the radii of curvature ($R_1$ and $R_2$) are purely geometric properties of the physical lens. They are fixed once the lens is manufactured and do not depend on the light passing through it.

Q: What is the practical consequence of this focal length difference?

Because different colors focus at different points, a simple lens cannot bring all colors to a sharp focus simultaneously. This creates color fringes around images, an optical defect known as chromatic aberration.

Q: Which color of light bends the most when passing through a glass lens?

Violet or blue light bends the most because it has the shortest wavelength in the visible spectrum, which corresponds to the highest refractive index in typical glass materials.

Q: Would this same effect happen if we used a curved mirror instead of a lens?

No! The focal length of a spherical mirror depends only on its radius of curvature ($f = R/2$) and is completely independent of the refractive index or the wavelength of light. Mirrors do not suffer from chromatic aberration.

Question

When monochromatic red light is used instead of blue light in a convex lens, its focal length will

Options:

(A) not depend on colour of light

(B) increase

(C) decrease

(D) remain same

Sigma Percentile · Accepted Answer

The behavior of light as it passes through a lens is one of the most fascinating topics in optics. When we shine different colors of light through the same convex lens, they don't all behave exactly the same way. In this problem, we are asked to determine what happens to the focal length of a convex lens when we switch from using monochromatic blue light to monochromatic red light. ### The Lens Maker's Formula To understand how a lens focuses light, we rely on the **Lens Maker's Formula**. This powerful equation connects the physical geometry of the lens to its optical properties: $$ \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2} ight) $$ Here, $f$ is the focal length, $\mu$ is the refractive index of the lens material, and $R_1$ and $R_2$ are the radii of curvature of the lens surfaces. Notice the crucial relationship here: the focal length $f$ is **inversely proportional** to the term $(\mu - 1)$. This means that if the refractive index $\mu$ increases, the focal length $f$ must decrease, and vice versa. ### Cauchy's Formula and Dispersion Now, we must ask ourselves: is the refractive index $\mu$ a constant for all types of light? The answer is no. The refractive index of a material depends on the wavelength $\lambda$ of the light passing through it. This relationship is described by **Cauchy's Formula**: $$ \mu = A + \frac{B}{\lambda^2} + \frac{C}{\lambda^4} + \dots $$ From this equation, we can see that the refractive index $\mu$ is roughly inversely proportional to the square of the wavelength $\lambda$. ### Comparing Red and Blue Light Let's look at the visible light spectrum. We know that red light has a longer wavelength than blue light: $$ \lambda_{ ext{blue}} < \lambda_{ ext{red}} $$ Because of the inverse relationship established by Cauchy's formula, a shorter wavelength corresponds to a higher refractive index. Therefore, the lens material bends blue light more than it bends red light: $$ \mu_{ ext{blue}} > \mu_{ ext{red}} $$ ### The Final Conclusion Let's bring these two concepts together. We know that blue light experiences a higher refractive index ($\mu_{ ext{blue}} > \mu_{ ext{red}}$). Going back to the Lens Maker's formula, since $f$ is inversely proportional to $(\mu - 1)$, a higher refractive index results in a shorter focal length. $$ f_{ ext{blue}} < f_{ ext{red}} $$ Therefore, when we replace blue light with red light, the refractive index decreases, which causes the focal length to **increase**. The red light will focus at a point further away from the lens compared to the blue light. This phenomenon is the root cause of **chromatic aberration** in simple lenses!

Animated Solution for Physics - Optics: When monochromatic red light is used instead of blue light in a convex lens, its focal length will

Select Answer:

Visualized Solution

The Setup

Lens Maker's Formula

Cauchy's Formula

Wavelength vs Refractive Index

Refractive Index vs Focal Length

Conclusion

Chromatic Aberration

The Sigma Insight: Lens

The Lens Maker's Formula

Cauchy's Formula and Dispersion

Comparing Red and Blue Light

The Final Conclusion

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