When you hold an insect at the near point of your eye it subtends an angle of 5.00 x 10^-3 rad. Determine the angular size (magnitude only) of the insect when viewed through a microscope that has an angular magnification with a magnitude of 145.

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To determine the angular size of the insect when viewed through the microscope, we first need to understand the concept of angular magnification.

Angular magnification is the ratio of the angle subtended by an object when viewed through a device, such as a microscope, to the angle subtended by the same object when viewed without the device. It tells us how much larger an object appears when viewed through the device compared to viewing it directly.

In this case, the angular magnification of the microscope is given as 145. This means that the microscope makes the insect appear 145 times larger than it appears when viewed directly.

Now, given that when the insect is held at the near point of your eye, it subtends an angle of 5.00 x 10^-3 rad, we can calculate the angular size of the insect when viewed through the microscope.

The angular size of the insect when viewed through the microscope can be calculated using the following formula:

Angular size = Angular magnification * Angular size when viewed directly

Substituting the values into the formula, we have:

Angular size = 145 * (5.00 x 10^-3 rad)

To get the answer, we simply multiply the angular magnification (145) by the angular size when viewed directly (5.00 x 10^-3 rad).

Calculating this gives us the angular size of the insect when viewed through the microscope, which is:

Angular size = 725 x 10^-3 rad

Therefore, the angular size of the insect when viewed through the microscope is 725 x 10^-3 rad.