Angular Magnification and the Magnifying Glass

[BoogieL80]

I'm having problems with the following problem:

A person who has a near point of 25.0 cm is looking with unaided eyes at an object that is located at the near point. The object has an angular size of 0.012 rad. Then, holding a magnifying glass (f= 10.0 cm) next to her eye, she views the image of this object , the image being located at the near point. What is the angular size of the image?

The answer is suppose to be 0.042 rad. However I'm getting a different answer. I used the formula M = (1/f - 1/d_i)N

I assumed that N = 25.0 cm
d_o = 25.0cm
M = 0.012 rad

For the first part and in the second part
f = 10.0 cm
d_i = -25.0cm

However when I plug in my numbers I get an answer of 3.5. What am I doing wrong?

 

[andrevdh]

It can be solved with just the basic formulas. First work out the height of the object from the given angle (0.012 rad) and distance (25 cm). Then get the object distance with the thin lens formula for the magnifying glass. Use the magnification of this setup to get the image height. From this one can calculate the angle that the image makes at the eye. The angles are small so one can approximate the radian angle calculations with height/(distance from eye).

 

[andrevdh]

The magnifation $M=3.5$ that you get is the ratio of the height of the image of the object to the real height of the object. You can work out the real height $h$ of the object with the $0.012\ rad$ angle. This and the magnification enables you to calculate the height of the image $h\prime$

 

[mekar]

Since magnification is 3.5, thus the image size is 0.3cm x 3.5 = 1.05 cm.
θ=〖tan〗^(-1) 1.05/25=2.405°=0.042rad

 

[rwisz]

It seems like you have misunderstood the formula for angular magnification. The correct formula is M = di/do, where di is the distance of the image from the lens and do is the distance of the object from the lens. In this problem, the object and image are both at the near point, so do = di = 25.0 cm.

Using this formula, we get M = 25.0 cm / 25.0 cm = 1. This means that the image is the same size as the object, so the angular size of the image is also 0.012 rad.

It's important to note that the angular magnification of the magnifying glass is not being used in this problem. The magnifying glass simply allows the person to see the image at their near point, which is why the image is located at the near point.

I hope this helps clarify the issue. Remember to always double check your formulas and make sure you are using the correct values for each variable. Good luck!