A student focuses the image of a candle flame, placed at about 2 m from a convex lens of focal length 10 cm, on a screen. After that he moves gradually the flame towards the lens and each time focuses its image on the screen. (A) In which direction does he move the lens to focus the flame on the screen? (B) What happens to the size of the image of the flame formed on the screen? (C) What difference is seen in the intensity (brightness) of the image of the flame on the screen? (D) What is seen on the screen when the flame is very close (at about 5 cm) to the lens?

Based on the principles of refraction through a convex lens of focal length $f = 10\text{ cm}$:

• (A) Direction of movement: As the candle flame is moved closer to the lens, the image distance ($v$) increases. To keep the image focused on the screen, the distance between the lens and the screen must increase. Therefore:
• If the screen is at a fixed position, the student must move the lens towards the candle flame (away from the screen).
• If the lens is at a fixed position, the student must move the screen away from the lens.

• (B) Size of the image: The size of the image of the flame increases gradually as the flame is brought closer to the focus of the lens.

• (C) Intensity of the image: The intensity (brightness) of the image decreases because the same amount of light energy is spread over a larger area as the image size increases.

• (D) Observation when flame is at $5\text{ cm}$: Since the object distance ($5\text{ cm}$) is less than the focal length ($10\text{ cm}$), the lens forms a virtual, erect, and magnified image behind the object. Since virtual images cannot be projected, no distinct image is formed on the screen; only a blurred patch of light is seen.