An observer with normal eyes views an object with magnifying glass of focal length 5 cm. the angular magnification is? [least distance of distinct vision D ...
An observer with normal eyes views an object with magnifying glass of focal length 5 cm. the angular magnification is? [least distance of distinct vision D = 25 cm]
Answer Details
When an observer views an object through a magnifying glass, the magnifying glass produces a virtual image of the object which is seen by the observer. The angular magnification is defined as the ratio of the angle subtended by the virtual image as seen through the magnifying glass to the angle subtended by the object when viewed with the unaided eye.
To calculate the angular magnification, we need to first find the position of the virtual image produced by the magnifying glass. We can use the lens formula:
1/f = 1/v - 1/u
where f is the focal length of the magnifying glass, u is the distance of the object from the magnifying glass, and v is the distance of the virtual image from the magnifying glass.
Since the observer is viewing the object with normal eyes, the distance of the object from the observer (u) is equal to the least distance of distinct vision (D), which is given as 25 cm.
Therefore,
1/0.05 = 1/v - 1/0.25
Simplifying, we get:
v = 0.0667 m
Now, we can calculate the angular magnification using the formula:
M = -v/u
where M is the angular magnification. The negative sign indicates that the image is inverted.
Substituting the values, we get:
M = -0.0667/0.25 = -0.2668
Therefore, the angular magnification is approximately -0.27, which is equivalent to -6 (since magnitudes are usually expressed as positive numbers).
So, the answer is (A) -6.