Respuesta :
If his near point is a typical 25cm, he must hold the gem that he is inspecting at 4.17cm in front of the magnifying lens (convex lens) that the jeweler is wearing.
What is convex lens?
This type of lens is thicker at the centre and thinner at the edges. An optical lens is generally made up of two spherical surfaces. If those surfaces are bent outwards, the lens is called a biconvex lens or simply a convex lens.
How to calculate, how close can he hold a gem that he is inspecting?
First, let's calculate the focal length of the lens.
f = 1 / P
= 1 / 20D
= 0.05m * ( 10^2 cm / 1m)
= 5cm
Convex lens will create a virtual image of a nearby object. Therefore, the image distance is taken as negative, di = -25cm
The position where the gem can be held is calculated with this formula :
1 / f = 1 / do + 1 / di
1 / do = 1 / f - 1 / di
= (1 / 5cm) - (1 / -25cm)
do = 4.17cm
Therefore, the jeweler needs to hold the gem at 4.17cm.
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