A point object is at 30 cm from a convex glass lens (μn=(3)/(2)) of focal length 20 cm. The fi

step 1 For this question, final image is formed in purity if the combination focal length of the two le

A point object is at 30 cm from a convex glass lens...

A point object is at $30 \mathrm{~cm}$ from a convex glass lens $\left(\mu_{n}=\frac{3}{2}\right)$ of focal length $20 \mathrm{~cm}$. The final image of object will be formed at infinity if (a) another concave lens of focal length $60 \mathrm{~cm}$ is placed in contact with the previous lens (b) another convex lens of focal length $60 \mathrm{~cm}$ is placed at a distance of $30 \mathrm{~cm}$ from the first lens (c) the whole system is immersed in a liquid of refractive index $4 / 3$ (d) the whole system is immersed in a liquid of refractive index $9 / 8$

A point object is at $30 \mathrm{~cm}$ from a convex glass lens $\left(\mu_{n}=\frac{3}{2}\right)$ of focal length $20 \mathrm{~cm}$. The final image of object will be formed at infinity if
(a) another concave lens of focal length $60 \mathrm{~cm}$ is placed in contact with the previous lens
(b) another convex lens of focal length $60 \mathrm{~cm}$ is placed at a distance of $30 \mathrm{~cm}$ from the first lens
(c) the whole system is immersed in a liquid of refractive index $4 / 3$
(d) the whole system is immersed in a liquid of refractive index $9 / 8$

Key Concepts

Refractive Index and Immersion Effects

The refractive index of the medium surrounding a lens affects its optical properties, including its focal length. Changing the surrounding medium effectively alters the refractive index contrast between the lens material and its environment, which can modify the focal length as predicted by the lens maker's formula. This concept is crucial when considering optical systems that operate in different environments.

Lens Combination (Effective Focal Length)

When two or more lenses are used together, their optical powers add to provide an effective focal length for the system. For lenses in contact, the effective focal length can be calculated using the sum of their individual powers, while for separated lenses, additional considerations of spacing are required.

Thin Lens Equation

This is a fundamental relation in geometric optics which connects the object distance, image distance, and the focal length of a lens. The equation is typically written as 1/f = 1/v + 1/u, and it is essential for determining the position and nature of images formed by lenses.

Focal Length Concept

Focal length is a key property of lenses and dictates how strongly they converge or diverge light. It is defined as the distance from the lens where parallel rays of light either converge (for convex lenses) or appear to diverge (for concave lenses) after refraction.

Image Formation at Infinity

When an image is formed at infinity, the refracted rays emerge parallel to each other. This concept is important in optics since it indicates that the object is placed at the lens’s focal point, and such a condition is useful in applications that require collimated light, such as telescopes and optical instruments.

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