Final answer:
To find the angular magnification of an image by a magnifying glass with a focal length of 5.0 cm and object distance of 4.0 cm, you calculate the image distance and use the magnification formula. The angular magnification when the lens is held close to the eye is 6. None of the options are correct.
Step-by-step explanation:
The question is asking to find the angular magnification of an image created by a magnifying glass when the object distance (do) and the focal length (f) of the lens are given.
In this case, do is 4.0 cm and f is 5.0 cm.
Using the lens formula 1/f = 1/do + 1/di, where di is the image distance, we can find di first.
The magnification equation for a lens is the magnification (M) = -di/do, where a negative sign indicates an inverted image and a positive one indicates an upright image.
Since magnifying glasses produce upright images, we expect a positive magnification value.
First, calculate di:
1/5 = 1/4 + 1/di
1/di = 1/5 - 1/4
1/di = -1/20
di = -20 cm (Here, the negative sign represents that the image is formed on the same side as the object, which is characteristic of a virtual, upright image produced by a magnifying glass.)
Now, calculate M:
M = -di/do
M = 20/4
M = 5