Unit 13: Geometric and Physical Optics
Weightage : 15–18%
A large lens is used to focus an image of an object onto a screen. If the left half of the lens is covered with a dark card, which of the following occurs?
Correct Answer: \( \boxed{\mathrm{D}} \)
Every small portion of a converging lens forms the entire image. Covering half of the lens does not remove half of the image because light from every point on the object can still pass through the uncovered portion of the lens.
Since only half as much light reaches the lens, the amount of light contributing to each image point decreases.
As a result, the image remains in focus and retains its full size, but its brightness decreases.
A blurred image would occur only if the lens were moved away from its correct focal position, not by blocking part of the lens.
Therefore, the correct answer is (D).
Two thin lenses each with a focal length of \(+10\,\mathrm{cm}\) are located \(30\,\mathrm{cm}\) apart with their optical axes aligned as shown. An object is placed \(35\,\mathrm{cm}\) from the first lens. After the light has passed through both lenses, at what distance from the second lens will the final image be formed?
Correct Answer: \( \boxed{\mathrm{C}} \)
Apply the thin lens equation to the first lens:
\( \frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}. \)
With \(f=10\,\mathrm{cm}\) and \(d_o=35\,\mathrm{cm}\),
\( \frac{1}{10}=\frac{1}{35}+\frac{1}{d_i}. \)
Solving,
\( d_i=14\,\mathrm{cm}. \)
This intermediate image is \(14\,\mathrm{cm}\) to the right of the first lens. Since the lenses are \(30\,\mathrm{cm}\) apart, this image is
\(30-14=16\,\mathrm{cm}\)
to the left of the second lens, so it acts as the object for the second lens.
For the second lens,
\( \frac{1}{10}=\frac{1}{16}+\frac{1}{d_i}. \)
Therefore,
\( \frac{1}{d_i}=\frac{1}{10}-\frac{1}{16}=\frac{3}{80}, \)
\( d_i=\frac{80}{3}\approx26.7\,\mathrm{cm}. \)
Thus, the final image is formed approximately \(27\,\mathrm{cm}\) to the right of the second lens.
Hence, the correct answer is (C).
A real object is located in front of a convex lens at a distance greater than the focal length of the lens. What type of image is formed and what is true of the image’s size compared to that of the object?
| Option | Type of Image | Size of Image |
|---|---|---|
| (A) | Real | Larger than object |
| (B) | Real | More information is needed |
| (C) | Virtual | Smaller than object |
| (D) | Virtual | Larger than object |
Correct Answer: \( \boxed{\mathrm{B}} \)
A convex lens is a converging lens. When a real object is placed at a distance greater than the focal length (\(d_o>f\)), the image formed is always real and inverted.
However, the size of the image depends on the object’s position relative to the focal point and the center of curvature (\(2f\)):
Since the problem states only that the object is farther than the focal length, there is not enough information to determine the image size.
Therefore, the image is real, but more information is needed to determine whether it is larger, smaller, or the same size as the object.
Hence, the correct answer is (B).
