Lensmaker's Formula: Solving for Image Distance i

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In summary, Lensmaker's Formula is a mathematical equation used to calculate the distance of an image created by a lens. It takes into account the properties of the lens, such as its focal length and curvature, and the distance of the object from the lens. To solve for the image distance <em>i</em>, you need to know the values for <em>n</em>, <em>R<sub>1</sub></em>, and <em>R<sub>2</sub></em> and plug them into the equation. However, the formula has limitations, as it is based on the thin lens approximation and does not account for aberrations and imperfections. Some real-world applications of Lensmaker's Formula include designing and producing
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jpartdq
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Homework Statement


A lens has a focal length of f=20cm. If an object is at o=50 cm, where is the image?



Homework Equations



1/f = 1/o + 1/i

The Attempt at a Solution



1/20 = 1/50 + 1/i

5/100 = 2/100 + 1/i

3/100 = 1/i

i = 100/3

I'm not sure how the answer could be 1/20 = 1/50 + 1/(100/3)? What am I doing wrong?
 
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  • #2
The answer is i=100/3 cm (i is the image distance). Why do you suspect it's wrong?
 
  • #3


Your approach is correct, but you have made a small mistake in the final step. Instead of dividing 1 by 100/3, you should be multiplying by the reciprocal, 3/100. This will give you the correct answer of i = 50 cm. Remember to always check your units and make sure they cancel out to give you the correct unit for your final answer. Keep up the good work!
 

What is Lensmaker's Formula?

Lensmaker's Formula is a mathematical formula used to calculate the distance of an image created by a lens. It takes into account the properties of the lens, such as its focal length and curvature, and the distance of the object from the lens.

What is the equation for Lensmaker's Formula?

The equation for Lensmaker's Formula is 1/i = (n-1)(1/R1 - 1/R2), where i is the image distance, n is the index of refraction of the lens material, and R1 and R2 are the radii of curvature of the lens surfaces.

How do you use Lensmaker's Formula to solve for image distance i?

To solve for i using Lensmaker's Formula, you will need to know the values for n, R1, and R2 for the specific lens you are using. Then, simply plug these values into the equation and solve for i.

What are the limitations of Lensmaker's Formula?

Lensmaker's Formula is based on the thin lens approximation, which assumes that the thickness of the lens is negligible compared to its focal length. This means that it may not be as accurate for lenses with a significant thickness. Additionally, the formula does not take into account factors such as aberrations and lens imperfections.

What are some real-world applications of Lensmaker's Formula?

Lensmaker's Formula is commonly used in the design and production of lenses for various optical instruments, such as cameras, microscopes, and telescopes. It is also used in the manufacturing of eyeglasses and contact lenses. In the field of ophthalmology, Lensmaker's Formula is used to determine the power of corrective lenses for individuals with vision impairments.

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