Optics - Angular Magnification

• Hyperfluxe
In summary: The first lens gets the light from the actual object first. So the first object distance would be 17cm.
Hyperfluxe

Homework Statement

The eyepiece of a compound microscope has a focal length of 2.50 cm and the objective has a focal length of 1.5 cm. The two lenses are separated by 17 cm. The microscope is used by a person with normal eyes (near point at 25 cm). What is the angular magnification of the microscope?

a) 283 x
b) 145 x
c) 97 x
d) 113 x
e) 242 x

Homework Equations

Angular Magnification = Near point / f (eye piece) = 25cm / f (eye piece)

Total magnification = 25cm(s1') / (f1f2)

The Attempt at a Solution

At first, I just thought it was asking for total magnification and got 113x, which is wrong. I know that the angular magnification is 25 / f (eye piece) so 25/2.5? Clearly not right. Perhaps I need to use the object-image formula (1/s + 1/s' = 1/f) to derive more information, but I'm not sure how. Help would be appreciated =)

Why did you use 25cm for the near-point in the formula?
How may the other two measurements be used?

Do you know how the total magnification is related to the angular magnification?

I used 25cm because that is the normal near point, and it says it in the problem statement. The total magnification = angular magnification * lateral magnification, where lateral magnification = s1'/s1
Since I know that the total magnification is 113.333 (as calculated in my original post), I just have to divide by the lateral magnification to get the angular magnification. I don't know which measurements to use for lateral magnification though...

Hyperfluxe said:
I used 25cm because that is the normal near point, and it says it in the problem statement.
<checks> Oh so it does - well done ;)
The total magnification = angular magnification * lateral magnification, where lateral magnification = s1'/s1
Since I know that the total magnification is 113.333 (as calculated in my original post), I just have to divide by the lateral magnification to get the angular magnification. I don't know which measurements to use for lateral magnification though...
How would you normally compute the lateral magnification in a system of two lenses?

Simon Bridge said:
How would you normally compute the lateral magnification in a system of two lenses?

Using the object-image relation formula (1/s + 1/s' = 1/f), the image from the first lens becomes the object of the second lens. I tried doing that, but I'm not sure which lens acts as the object, and would the first object distance be 17cm?

You are doing well - see how these questions refine the problem by stages?
Which lens gets the light from the actual object first?

What is angular magnification?

Angular magnification is a measure of how much larger an object appears when viewed through a lens or optical instrument compared to when viewed with the naked eye. It is a measure of the apparent size of an object, rather than its actual size.

How is angular magnification calculated?

Angular magnification is calculated by dividing the angle subtended by the image formed by the lens or optical instrument by the angle subtended by the object when viewed with the naked eye. This ratio can also be expressed as the ratio of the image distance to the object distance.

What factors affect angular magnification?

The most significant factor that affects angular magnification is the focal length of the lens or optical instrument. A longer focal length will result in a larger angular magnification, while a shorter focal length will result in a smaller angular magnification. The distance between the object and the lens or instrument can also affect the angular magnification, with a larger distance resulting in a smaller magnification.

How does angular magnification relate to image size?

Angular magnification is directly related to image size. A larger angular magnification will result in a larger image size, while a smaller angular magnification will result in a smaller image size. This is because the larger the angular magnification, the more the image is magnified compared to the object.

What are some common applications of angular magnification?

Angular magnification has many practical applications, including in binoculars, telescopes, and microscopes. It is also used in photography to determine the zoom level of a lens. In addition, angular magnification is important in vision correction, such as in eyeglasses or contact lenses, to magnify or reduce the apparent size of objects for individuals with vision impairments.

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