Question

Write using simplified rational exponent.

Answer 1

The type of magnification that compares the angular size of an image to the angular size of an object, assuming a reference distance of 25 cm, is angular magnification.

Step-by-step explanation:

Angular magnification
`(\(M\))` is defined as the ratio of the angle subtended by the image
`(\(\theta_i\))` to the angle subtended by the object
`(\(\theta_o\))` when viewed from a specific reference distance. Mathematically, it is expressed as
`\(M = (\theta_i)/(\theta_o)\)`. The reference distance is often taken as 25 cm.

In the case of optical instruments, such as microscopes or telescopes, the angular magnification can be calculated using the formula
`\(M = \frac{L_{\text{final}}}{f}\)`, where
`\(L_{\text{final}}\)` is the final image distance and
`\(f\)` is the focal length. The angle subtended by the object
`(\(\theta_o\))` is related to the object's size
`(\(h\))` and its distance from the observer
`(\(d_o\))` through the tangent function:
`\(\tan(\theta_o) = (h)/(d_o)\)`.

To elaborate, consider a scenario where a microscope with a focal length of 1 cm is used to observe an object placed 2 cm away. The angle subtended by the object
`(\(\theta_o\))` is given by
`\(\tan(\theta_o) = (h)/(d_o)\)`, and the angular magnification
`(\(M\))` is calculated using
`\(M = \frac{L_{\text{final}}}{f}\)`. This example showcases how angular magnification compares the angular size of an image to that of an object at a specific reference distance, allowing for precise observations in microscopy and astronomy.