The near point of a naked eye is 32 cm. When an object is placed at the near point and viewed by the naked eye, it has an angular size of 0.068 rad. A magnifying glass has a focal length of 15 cm, and is held next to the eye. The enlarged image that is seen is located 63 cm from the magnifying glass. Determine the angular size of the image.

To determine the angular size of the image seen through the magnifying glass, we need to use the concept of angular magnification. The angular magnification, M, can be calculated using the formula:

M = (1 + d/f) * (D/25)

Where:
d is the distance between the object and the near point (32 cm in this case).
f is the focal length of the magnifying glass (15 cm in this case).
D is the distance between the image and the magnifying glass (63 cm in this case).

Plugging in the values, we get:

M = (1 + 32/15) * (63/25)
M = 2.133 * 2.52
M = 5.375

So, the angular magnification is 5.375.

Now, to calculate the angular size of the image, we divide the angular size of the object by the angular magnification:

Angular size of the image = Angular size of the object / Angular magnification

Angular size of the image = 0.068 rad / 5.375

Angular size of the image = 0.01267 rad

Therefore, the angular size of the image seen through the magnifying glass is approximately 0.01267 radians.