A convex lens has a focal length of 15 cm. As shown in the diagram, the lens is placed on a laboratory table using a stand. A lit candle is placed 20 cm away from the lens. (i) (a) Draw a ray diagram showing how the image of the candle flame is formed. (b) State three characteristics of the image. (c) State a device that uses such an image. (ii) Consider the case where this lens is used as a magnifying glass to observe a small insect. (a) Within what range of distance from the lens should the insect be placed? (b) Can you obtain the image of the insect you are observing on a screen? (c) State the reason for your answer in (ii) (b) above.

1. Problem Description

A convex lens has a focal length of 15 cm. As shown in the diagram, the lens is placed on a laboratory table using a stand. A lit candle is placed 20 cm away from the lens.

(i) (a) Draw a ray diagram showing how the image of the candle flame is formed.

(b) State three characteristics of the image.

(c) State a device that uses such an image.

(ii) Consider the case where this lens is used as a magnifying glass to observe a small insect.

(a) Within what range of distance from the lens should the insect be placed?

(b) Can you obtain the image of the insect you are observing on a screen?

(c) State the reason for your answer in (ii) (b) above.

2. Solution Steps

(i) (a) Ray Diagram:

The ray diagram should show the following:

- A ray from the top of the flame parallel to the principal axis, refracting through the lens and passing through the focal point on the other side.

- A ray from the top of the flame passing through the optical center of the lens, continuing straight.

- The intersection of these two rays indicates the location of the image.

- The image will be real, inverted and magnified.

(i) (b) Characteristics of the Image:

Since the object distance ($u = 20 cm$) is greater than the focal length ($f = 15 cm$) but less than twice the focal length ($2f = 30 cm$), the image will be real, inverted, and magnified. Let's calculate the image distance $v$ using the lens formula:

$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

$\frac{1}{15} = \frac{1}{20} + \frac{1}{v}$

$\frac{1}{v} = \frac{1}{15} - \frac{1}{20} = \frac{4 - 3}{60} = \frac{1}{60}$

$v = 60 cm$

Magnification, $m = \frac{v}{u} = \frac{60}{20} = 3$

Therefore, the characteristics are:

1. Real

2. Inverted

3. Magnified (3 times the object size)

(i) (c) Device that Uses Such an Image:

A projector uses a real, inverted, and magnified image.

(ii) (a) Distance Range for Insect Observation:

For the lens to act as a magnifying glass, the insect must be placed within the focal length of the lens. Therefore, the insect should be placed at a distance less than 15 cm from the lens.

(ii) (b) Can the Image be Obtained on a Screen?

No, you cannot obtain the image on a screen when using the lens as a magnifying glass.

(ii) (c) Reason:

When the object is placed within the focal length, the image formed is virtual, erect, and magnified. Virtual images cannot be projected onto a screen because the light rays do not actually converge at a point to form the image. Instead, the rays appear to come from a point behind the lens.

3. Final Answer

(i) (a) A ray diagram showing the formation of a real, inverted, and magnified image at 60cm on the other side of the lens.

(i) (b)

1. Real,

2. Inverted,

3. Magnified

(i) (c) Projector

(ii) (a) Less than 15 cm

(ii) (b) No

(ii) (c) The image formed is virtual. Virtual images cannot be obtained on a screen.