Final answer:
A 15.0 cm focal length magnifying glass produces a virtual image when held 13.5 cm from a mole. The magnification is 2.67 times, resulting in an image size of 13.35 mm for a 5.00 mm mole.
Step-by-step explanation:
When a doctor examines a mole with a 15.0 cm focal length magnifying glass held 13.5 cm from the mole, the following calculations can be made:
(a) Where is the image?
For a magnifying glass, the image is virtual and located on the same side as the object. Since the object is closer to the focal point than the lens, the image will be at a distance greater than the focal length from the lens. The exact position can't be determined with the information given, as the lens equation would yield a negative image distance, indicating a virtual image.
(b) What is its magnification?
The magnification (M) of the image produced by a magnifying glass is given by the equation:
M = 1 + (D/f)
where:
D = 25 cm (near point of the average human eye) and
f = focal length of the magnifying glass. Plugging in our values:
M = 1 + (25 cm / 15 cm) = 1 + (5/3)
= 1 + 1.67
= 2.67
(c) How big is the image of a 5.00 mm diameter mole?
To find the size of the image, multiply the actual size by the magnification:
Image size = Actual size x Magnification
Image size = 5.00 mm x 2.67
Image size = 13.35 mm
The image of the mole would be 13.35 mm in diameter when inspected through the magnifying glass.