Explanation:

Apposition image in cockroach refers to the formation of an image by the compound eyes of a cockroach. The compound eyes consist of numerous ommatidia, each of which has a lens that focuses light onto photoreceptor cells. The photoreceptor cells convert the light into neural signals that are sent to the brain, where they are interpreted as an image.

Bright Light:

In bright light, the apposition image in cockroach is formed due to the following reasons:

- The lenses in the ommatidia of the compound eyes focus the light onto the photoreceptor cells, resulting in a clear and sharp image.
- The photoreceptor cells are able to detect the high intensity of light and generate strong neural signals that are sent to the brain.
- The brain processes the signals and creates a high-resolution image that allows the cockroach to navigate and avoid obstacles.

Dim Light:

In dim light, the apposition image in cockroach is not formed because:

- The low intensity of light does not provide enough energy to activate the photoreceptor cells.
- The lenses in the ommatidia are not able to focus the light onto the photoreceptor cells, resulting in a blurry and unfocused image.
- The brain receives weak neural signals and is unable to create a clear image.

Total Darkness:

In total darkness, the apposition image in cockroach is not formed because:

- There is no light for the lenses to focus onto the photoreceptor cells.
- The photoreceptor cells are not activated and do not generate any neural signals.
- The brain does not receive any signals and is unable to create an image.

Conclusion:

Thus, the apposition image in cockroach is formed in bright light because the lenses in the ommatidia are able to focus the light onto the photoreceptor cells, resulting in a clear and sharp image. In dim light and total darkness, the apposition image is not formed due to the lack of energy and activation of the photoreceptor cells.