Chapter 38, Problem 15SP

Draw diagrams to indicate qualitatively the position, nature, and size of the image formed by a converging lens of focal length f for the following object distances: (a) infinity, (b) greater than 2f, (c) equal to 2f, (d) between 2f and f, (e) equal to f, (f) less than f.

To determine

The position, nature, and size of the image formed by a converging lens of focal length $f$ for the object distance of infinity.

Answer to Problem 15SP

Solution:

The image is formed at the focus and is inverted, real, and highly diminished.

Explanation of Solution

Introduction:

Employ the rules of ray diagram for a convex lens to determine the position, nature, and size of the image formed.

Explanation:

The resulting ray diagram for an object kept at infinity is drawn below:

From the ray diagram given above, it is clear that the image is formed at the focus and is inverted, real, and highly diminished.

Conclusion:

Therefore, when the object is kept at an infinite distance from the lens, the image is formed at the focus and is inverted, real, and highly diminished.

To determine

The position, nature, and size of the image formed by a converging lens of focal length $f$ for object distance greater than $2f$.

Answer to Problem 15SP

Solution:

The image is formed between $f$ and $2f$, and is inverted, real, and diminished.

Explanation of Solution

Introduction:

Employ the rules of ray diagram for a convex lens to determine the position, nature, and size of the image formed.

Explanation:

The resulting ray diagram for an object kept at a distance greater than $2f$ is drawn below:

From the ray diagram given above, it is clear that the image is formed between $f$ and $2f$, and is inverted, real, and diminished.

Conclusion:

Therefore, when the object is kept at a distance greater than $2f$, the image is formed between $f$ and $2f$, and is inverted, real, and diminished.

To determine

The position, nature, and size of the image formed by a converging lens of focal length $f$ for an object distance equal to $2f$

Answer to Problem 15SP

Solution:

The image is formed at $2f$ and is inverted, real, and of the same size as the object.

Explanation of Solution

Introduction:

Use the rules of ray diagram for a convex lens to determine the position, nature, and size of the image formed when the object is placed at $2f$.

Explanation:

The resulting ray diagram for an object kept at a distance of $2f$ is drawn below:

From the ray diagram given above, it is clear that the image is formed at $2f$, and is inverted, real, and of the same size as the object.

Conclusion:

Therefore, then the object is kept at a distance of $2f$, image is formed at $2f$ and is inverted, real, and of the same size as the object.

To determine

The position, nature, and size of the image formed by a converging lens of focal length $f$ for an object at a distance between $2f\text{ and }f$

Answer to Problem 15SP

Solution:

The image is formed beyond $2f$ and is inverted, real, and magnified.

Explanation of Solution

Introduction:

Here, we shall employ the rules of ray diagram for a convex lens to determine the position, nature, and size of the image formed.

Explanation:

The resulting ray diagram for an object kept at a distance between $2f\text{ and }f$ is drawn below:

From the ray diagram given above, it is clear that the image is formed beyond $2f$, and is inverted, real, and magnified.

Conclusion:

Therefore, when the object is kept at a distance between $2f\text{ and }f$, image is formed beyond $2f$ and is inverted, real, and magnified.

To determine

The position, nature, and size of the image formed by a converging lens of focal length $f$ for the object placed at distance $f$.

Answer to Problem 15SP

Solution:

The image is formed at infinity and is erect, virtual, and magnified.

Explanation of Solution

Introduction:

Use the rules of ray diagram for a convex lens to determine the position, nature, and size of the image formed, when the object is kept at a distance $f$.

Explanation:

The resulting ray diagram for an object kept at a distance $f$ is drawn below:

From the ray diagram given above, it is clear that the image is formed at infinity and is erect, virtual, and magnified.

Conclusion:

Therefore, when the object is kept at a distance $f$, the image is formed at infinity and is erect, virtual, and magnified.

To determine

The position, nature, and size of the image formed by a converging lens of focal length $f$ for an object distance less than $f$.

Answer to Problem 15SP

Solution:

The image is formed beyond $f$ and is erect, virtual, and magnified.

Explanation of Solution

Introduction:

Here, we shall employ the rules of ray diagram for a convex lens to determine the position, nature, and size of the image formed.

Explanation:

The resulting ray diagram for an object kept at a distance less than $f$ is drawn below:

From the ray diagram given above, it is clear that the image is formed beyond $f$ and is erect, virtual, and magnified.

Conclusion:

Therefore, when the object is kept at a distance less than $f$, the image is formed beyond f and is erect, virtual, and magnified.