Give the formula for calculating each of the following (2 points): Minification gain Brightness gain
The Correct Answer and Explanation is:
1. Minification Gain Formula
Minification gain refers to the reduction in the size of an optical image (such as in telescopes or microscopes), making the image appear smaller while retaining the resolution.
The formula for Minification Gain is:Minification Gain=Image SizeObject Size\text{Minification Gain} = \frac{\text{Image Size}}{\text{Object Size}}Minification Gain=Object SizeImage Size
Where:
- Image Size is the size of the image formed by the optical system.
- Object Size is the actual size of the object being viewed.
In simple terms, this formula measures how much smaller the image is compared to the original object. For example, in a microscope, a high minification gain indicates that the object is being magnified into a smaller field of view, helping focus on smaller details.
2. Brightness Gain Formula
Brightness gain is a measure of how much brighter an image appears due to an optical system, particularly in the case of telescopes or microscopes. This can occur because of the optical system’s ability to gather more light or direct light more efficiently.
The formula for Brightness Gain is:Brightness Gain=(Objective Lens AreaEyepiece Lens Area)\text{Brightness Gain} = \left(\frac{\text{Objective Lens Area}}{\text{Eyepiece Lens Area}}\right)Brightness Gain=(Eyepiece Lens AreaObjective Lens Area)
Where:
- Objective Lens Area is the area of the objective lens (the part that gathers light from the object).
- Eyepiece Lens Area is the area of the eyepiece lens (the part through which the image is viewed).
Another way to calculate brightness gain is to consider the ratio of the aperture areas, which determines how much light enters the system and reaches the observer. The formula in this context would be:Brightness Gain=Aperture Area of the ObjectiveAperture Area of the Eyepiece\text{Brightness Gain} = \frac{\text{Aperture Area of the Objective}}{\text{Aperture Area of the Eyepiece}}Brightness Gain=Aperture Area of the EyepieceAperture Area of the Objective
Explanation
- Minification Gain primarily affects the size of the field of view. A higher minification means the object appears smaller but with more detail and resolution.
- Brightness Gain is related to the optical system’s efficiency in gathering and transmitting light. A higher brightness gain means the image will appear brighter, which is crucial in low-light conditions for instruments like telescopes or microscopes.
