Calculating Focal Length of Parabolic Mirror with 5 Rays

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In summary, the conversation discusses a parabolic mirror with the equation x=-1/2y^2 and 5 parallel rays coming into the mirror at different points. The focal length is found using the equation f=D^2/(16c) where D is the diameter and c is the depth. The laws of reflection and geometric properties are used to solve for the focal length, with the suggestion to look for the point where the tangent is at 45°.
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J.Friedrich
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i have a parabolic mirror with equation x=-1/2y^2
there are 5 parallel rays coming into the parabolic mirror at y=2,y=1,y=0,y=-1,y=-2
(a) find the focal length


i found the equation f=D^2/(16c) where D is the diameter, and c is the depth.
this gives me a focal length of (1/2)

i was hoping some one could show me how to solve for the focal length by using the laws of reflection and the geometric properties of the problem

any help would be appreciated thanks
 
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Welcome to PF!

Hi J.Friedrich! Welcome to PF! :smile:

(try using the X2 icon just above the Reply box :wink:)
J.Friedrich said:
i was hoping some one could show me how to solve for the focal length by using the laws of reflection and the geometric properties of the problem

You know that lines parallel to the x-axis will be reflected onto the focus …

the easiest one to go for is the one that's reflected at right-angles …

so look for the point where the tangent is at 45°. :wink:
 

FAQ: Calculating Focal Length of Parabolic Mirror with 5 Rays

1. What is the formula for calculating the focal length of a parabolic mirror with 5 rays?

The formula for calculating the focal length of a parabolic mirror with 5 rays is f = R/2, where f is the focal length of the mirror and R is the radius of curvature of the parabola.

2. How do you determine the position of the focal point using 5 rays?

To determine the position of the focal point using 5 rays, you will need to draw 5 parallel rays, 3 of which will be parallel to the principal axis and will reflect off the mirror and converge at the focal point. The other two rays will pass through the focal point and reflect back parallel to the principal axis. The point where these 5 rays intersect will be the position of the focal point.

3. Can you use more or less than 5 rays to calculate the focal length of a parabolic mirror?

Yes, you can use more or less than 5 rays to calculate the focal length of a parabolic mirror. However, using 5 rays is the most common and efficient method as it provides a good approximation of the focal length while being relatively easy to draw and measure.

4. What factors can affect the accuracy of the focal length calculation using 5 rays?

The accuracy of the focal length calculation using 5 rays can be affected by several factors, such as the curvature of the mirror, the angle of incidence of the rays, and the precision of measuring the position of the focal point. Other factors such as imperfections in the mirror's surface and the wavelength of light can also affect the accuracy to some degree.

5. How can the focal length of a parabolic mirror be used in practical applications?

The focal length of a parabolic mirror is a crucial parameter in various practical applications, such as telescopes, satellite dishes, and solar cookers. It is also used in designing and optimizing optical systems for various purposes, including microscopy, photography, and laser technology.

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