Question

List two properties of the image formed by the lens B in case no. 2.

Answer 1

To determine the properties of the image formed by lens B in case no. 2, we use the given data:

Lens B:
Focal length (f) = 20 cm
Object distance (u) = –60 cm (object is placed on the left side of the lens, so it is taken as negative)

Since the object is placed beyond 2F (i.e., beyond 2 × 20 = 40 cm), this situation falls under the standard case where the object is placed beyond twice the focal length of a convex lens.

Two properties of the image formed:
1. The image is formed between F and 2F on the opposite side of the lens.
2. The image is real, inverted, and smaller in size (diminished).

Therefore, the image formed by lens B is a real and inverted image that is smaller than the object and located between the focus and twice the focal length on the other side of the lens.

Answer 2

The lens will form a real image of the same size as the object in Case No. 3, which involves lens C.

Given in Case 3:
Focal length of lens C = 15 cm
Object distance = 30 cm

When the object is placed at a distance equal to twice the focal length (i.e., at 2F) from a convex lens, the image formed has the following properties:
- It is formed at a distance of 2F on the other side of the lens
- It is real and inverted
- It is of the same size as the object

In Case 3, the object is placed at 30 cm, which is exactly 2 × focal length (2 × 15 cm = 30 cm). Hence, this matches the condition for forming a real image of the same size.

Conclusion: In Case No. 3, the lens forms a real and inverted image of the same size as the object because the object is placed at a distance equal to twice the focal length from the convex lens.

Answer 3

The type of lens used by opticians for the correction of hypermetropia (also known as farsightedness) is a convex lens, also called a converging lens.

Role of convex lens in correcting hypermetropia:
Hypermetropia is a vision defect in which a person can see distant objects clearly but finds it difficult to see nearby objects. This happens because the image of nearby objects is formed behind the retina instead of on it. This defect usually occurs due to either:
- A shorter than normal eyeball, or
- A less curved eye lens, reducing its converging power

To correct this defect, a convex lens is placed in front of the eye. This lens converges the light rays coming from nearby objects before they enter the eye. As a result, the rays are focused exactly on the retina, allowing the person to see nearby objects clearly.

Therefore, convex lenses help in shifting the image forward onto the retina by providing additional focusing power, thereby correcting the vision of a person with hypermetropia.

Answer 4

Lens formula calculation:

The lens formula is:

\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]

where:

• \(v =\) image distance
• \(u =\) object distance (\(-25 \, \text{cm}\), negative because it’s on the left side)
• \(f =\) focal length (\(50 \, \text{cm}\))

Substituting the values:

\[ \frac{1}{v} - \frac{1}{-25} = \frac{1}{50} \]

\[ \frac{1}{v} = \frac{1}{50} - \frac{1}{25} = \frac{1 - 2}{50} = -\frac{1}{50} \]

\[ v = -50 \, \text{cm} \]

The image distance is \(-50 \, \text{cm}\). The negative sign indicates that the image is virtual and forms on the same side as the object. This is not a real image, as stated before. There is an error in the problem statement as a real image is not possible in this case.