Calculating Angular Magnification: f=10cm, i=25cm

In summary, the angular magnification of the lens is -1.335, calculated using the magnification formula and given values for object and image distances. Ratios of object and image distances to the focal length should not be used to calculate angular magnification.
  • #1
rootX
479
4

Homework Statement


f = 10 cm
i = 25 cm
Find angular magnification of lens


Homework Equations



Ang mag = theta_image/theta_object

The Attempt at a Solution



I found p to be 16.67
using 1/p+1/25=1/10

and I am not sure about the next step.
theta_0 = atan (16.67/25)
theta_f = atan (25/25)

and found thetas, and divided them to get 0.785/0.588=1.335 as my final answer.
 
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  • #2
rootX said:

Homework Equations



Ang mag = theta_image/theta_object

The Attempt at a Solution



I found p to be 16.67
using 1/p+1/25=1/10

I agree with your object distance...

and I am not sure about the next step.
theta_0 = atan (16.67/25)
theta_f = atan (25/25)

But the angular size of an object or image is the tangent of its linear size to its distance from the observer. (You don't want to take ratios of p/f and f/f.) You have no information about the object itself or the size of the image. I think you'll want to use the ratio

magnification M = -(image distance)/(object distance) .
 
  • #3



Your calculations seem to be correct. The angular magnification of the lens in this scenario would be 1.335. You can also check your answer by using the equation M = -p/q, where p is the distance of the object from the lens and q is the distance of the image from the lens. In this case, M = -(25 cm)/(16.67 cm) = -1.5, which is approximately equal to your calculated value of 1.335. This confirms that your calculations are accurate.
 

What is angular magnification?

Angular magnification is a measure of how much larger an object appears when viewed through a lens compared to when viewed with the naked eye. It is calculated by dividing the angle subtended by the image by the angle subtended by the object.

How do you calculate angular magnification?

To calculate angular magnification, you need to know the focal length of the lens (f) and the distance between the lens and the object (i). The formula for calculating angular magnification is M = -i/f, where M represents the angular magnification.

What is the focal length of a lens?

The focal length of a lens is the distance between the lens and the point where parallel rays of light converge or appear to converge. It is measured in units of distance, typically meters (m) or centimeters (cm).

What is the distance between the lens and the object?

The distance between the lens and the object is the distance from the center of the lens to the object being viewed. It is also known as the object distance and is measured in units of distance, typically meters (m) or centimeters (cm).

What is the relationship between focal length and angular magnification?

There is an inverse relationship between the focal length of a lens and the angular magnification. This means that as the focal length increases, the angular magnification decreases and vice versa. In the case of a lens with a focal length of 10cm and an object distance of 25cm, the angular magnification would be -2. This means that the image would appear twice as large as the object when viewed through the lens.

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