Relationship between brightness of the image and magnifying power
The brightness of an image seen through a magnifying glass is directly related to its magnifying power.

Directly proportional relationship
When we say that the brightness of the image is directly proportional to the magnifying power, it means that as the magnifying power increases, the brightness of the image also increases. This is because a higher magnifying power allows more light to enter the eye, resulting in a brighter image.

Inversely proportional relationship
If the brightness of the image were inversely proportional to the magnifying power, it would mean that as the magnifying power increases, the brightness of the image decreases. However, this is not the case in reality.

Variation directly as the square of
It is more accurate to say that the brightness of the image varies directly as the square of the magnifying power. This means that if the magnifying power is doubled, the brightness of the image will be four times greater. This relationship is due to the fact that the amount of light entering the eye is directly related to the area of the lens through which the light passes.

Variation inversely as the square of
If the brightness of the image were to vary inversely as the square of the magnifying power, it would mean that as the magnifying power increases, the brightness of the image decreases by the square of the magnifying power. However, this is not the case in practice.
In conclusion, it is important to understand the correct relationship between the brightness of an image and the magnifying power to accurately interpret the visual experience when using a magnifying glass.