Finding Magnification of a Gem Using a Converging Lens

[mustang]

problem 24. A person looks at a gem using a concverging lense with a focal length of 13.7 cm. The lense forms a virtual image 35.5 cm from the lense.
a) Find the magnifaction.
This is what I have done so far:
f=13.7 , q= -35.5
1/p+1/q=1/f
1/f-1/q=1/p
1/13.7-(-1/35.5)=9.88516=p
M=-q/p
=--35.5/9.88516
= 4.02333

Is this right??

Problem 30. A magnifying glass has a converging lens of focal length 17.4 cm. At what distance from a nickel should you hold this lens to get an image with a magnificaiton of +2.06? Abswer in cm.
got p=8.7 and M=1.841932169 is this right?

Problem 32. A microscope slide is placed in front of a converging lens with a focal length of 3.48 cm. The lens forms an image of the slide 13.8 cm from the lens.
How far is the lens from the slide if the image is real? Answer in cm.

 

[Doc Al]

problem 24. A person looks at a gem using a concverging lense with a focal length of 13.7 cm. The lense forms a virtual image 35.5 cm from the lense.
a) Find the magnifaction.
This is what I have done so far:
f=13.7 , q= -35.5
1/p+1/q=1/f
1/f-1/q=1/p
1/13.7-(-1/35.5)=9.88516=p
M=-q/p
=--35.5/9.88516
= 4.02333

Is this right??

Your method is correct, but your answer is not. (Everything is correct except the last line.) Must have an arithmetic mistake. (Don't give so many significant figures in the answer: 3 is plenty.)

Problem 30. A magnifying glass has a converging lens of focal length 17.4 cm. At what distance from a nickel should you hold this lens to get an image with a magnificaiton of +2.06? Abswer in cm.
got p=8.7 and M=1.841932169 is this right?

I get a slightly different answer for p. M is given, so what does that answer mean?

 

[M98Ranger]

To find the magnification of a gem using a converging lens, we can use the formula M = -q/p, where M represents the magnification, q is the distance of the virtual image from the lens, and p is the distance of the object from the lens. In this case, we have f = 13.7 cm, q = -35.5 cm, and we need to find p, which we can do using the thin lens equation: 1/f = 1/p + 1/q. Plugging in the values, we get 1/13.7 = 1/p + 1/-35.5, which simplifies to p = 9.89 cm. Then, using the magnification formula, we get M = -(-35.5)/9.89 = 3.59, which means the magnification of the gem is 3.59 times its original size.

For problem 30, we can use the same formula, but this time we have M = 2.06 and f = 17.4 cm. We need to find p, so we rearrange the formula to get p = -q/M. Plugging in the values, we get p = -8.7/2.06 = -4.22 cm. Since the distance cannot be negative, we can assume that the lens should be held 4.22 cm away from the nickel to get an image with a magnification of 2.06.

For problem 32, we are given that the image formed is real, which means p is positive. We can use the same formula as before, but this time we have M = -q/p = -13.8/3.48 = -3.96. This means that the magnification of the slide is 3.96 times its original size. To find the distance between the lens and the slide, we can rearrange the thin lens equation to get 1/p = 1/f - 1/q. Plugging in the values, we get 1/p = 1/3.48 - 1/13.8, which simplifies to p = 5.83 cm. Therefore, the lens is 5.83 cm away from the slide.