When you hold an insect at the near point of your eye it subtends an angle of 5.00 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.
what is 145x5E-3 ?
To determine the angular size of the insect when viewed through a microscope, we need to consider the angular magnification of the microscope.
Angular magnification is given by the formula:
M = (θ' / θ)
Where M is the angular magnification, θ' is the angular size of the image formed by the microscope, and θ is the angular size of the object (insect) when viewed without the microscope.
We are given that the insect subtends an angle of 5.00 x 10^(-3) rad at the near point of the eye (without the microscope).
Now, we can rearrange the formula to solve for θ':
θ' = M * θ
Plugging in the values:
M = 145 (angular magnification of the microscope)
θ = 5.00 x 10^(-3) rad
θ' = 145 * (5.00 x 10^(-3))
= 725 x 10^(-3)
= 7.25 x 10^(-1) rad
Therefore, the angular size of the insect when viewed through the microscope is approximately 7.25 x 10^(-1) radians.