Focal length to get clear image

In summary, Harris needs to take a picture of a bird located at point B, but there is a wall in between. He directs his camera to a mirror located 3.7 m north from his position. The focal length of his camera can be calculated using the equation 1/f = 1/do + 1/di, where f is the focal length, do is the distance of the object (AB'), and di is the distance of the image. Harris can find the distance of AB' by using the Pythagorean theorem and can determine the image distance by extending the line from the camera to the mirror and using simple algebra. This question may require specialized camera knowledge, but it is likely for an introductory physics class.
  • #1
songoku
2,283
322

Homework Statement


aaav_zps3af9b4f7.png


Harris stands at point A and wants to take a picture of bird located at point B. Because there is wall, he has to direct his camera to mirror located 3.7 m to the north from his position. What is the focal length of his camera so that he can take a clear picture of the bird?

Homework Equations


1/f = 1/do + 1/di

f = focal length
do = distance of object
di = distance of image

The Attempt at a Solution


Harris will see the object as if it appears behind the mirror, let say at position B' (reflection of point B to the mirror), with distance 2.1 m. I try to find object distance (AB') by using Pythagorean theorem (triangle ABB'):

(4.3)2 + (3.7 + 2.1)2 = (BB')2

Is it true the object distance is BB'? If yes, then how to find the distance of image (di)? We have to know di first if we want to calculate f.

Thanks
 
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  • #2
songoku said:
(4.3)2 + (3.7 + 2.1)2 = (BB')2
Where did you get that? You need to show your work, not just write down an equation that doesn't seem to mean anything.
 
  • #3
phinds said:
Where did you get that? You need to show your work, not just write down an equation that doesn't seem to mean anything.

asfsd.JPG


Sorry, I just realized I made mistake.
O is the point on mirror where OB is perpendicular to mirror.
P is point where the light hits the mirror.
OB' is the reflection of OB to the mirror.
A' is point where A is reflected through the wall.

My guess is AB' is the distance of object for the equation. I just realized that AB' may not be a straight line so AA'B' may be not a right - angle triangle at A'. So, I don't know how to find the distance of object and distance of image.
 
  • #4
Hint: angle of incidence = angle of reflection.
 
  • #5
phinds said:
Hint: angle of incidence = angle of reflection.

The angle of incidence is tan-1 (2.15 / 3.7) = 30.2o.

Am I correct to say that the object distance is AB'? And what should be the image distance (I mean the distance from what point to what point that will be the image distance)?

Thanks
 
  • #6
Extend the line from the camera to the mirror to a point behind the mirror, then it's just Pythagoras and some simple algebra.
 
  • #7
phinds said:
Extend the line from the camera to the mirror to a point behind the mirror, then it's just Pythagoras and some simple algebra.

Ok I got the distance of AB', which is the object distance. To find the focal length of the camera, I have to know the image distance. What is the image distance? Is there special condition for it for getting clear image, such as the image must be formed at normal near point of eye?

Thanks
 
  • #8
What do you think? Do you think you might be able to Google "focal length of a camera" ?
 
  • #9
phinds said:
What do you think? Do you think you might be able to Google "focal length of a camera" ?

I tried but I found nothing, or maybe I just didn't understand that I had found the answer through google. What I found mostly the information related to aperture, shutter speed, etc.

I didn't think I had learn that there is special condition to obtain clear image for camera. If the object is really far, the image will be formed on focus point. But for object located at certain position, we adjusted the image distance so that we can obtain clear image. So I don't know how to find the image distance.

Thanks
 
  • #10
Fair enough. I'm not a camera guy so if they use something other than simple geometry, I'm lost. I was trying to help you solve a geometry problem that really had nothing to do with cameras. What was the context of the question/problem? Is it likely that it included the need for specialized camera knowledge? I would find that surprising if this was for a geometry or algebra class (or introductory physics) but maybe it would be normal if it's for a camera class.
 
  • #11
phinds said:
Fair enough. I'm not a camera guy so if they use something other than simple geometry, I'm lost. I was trying to help you solve a geometry problem that really had nothing to do with cameras. What was the context of the question/problem? Is it likely that it included the need for specialized camera knowledge? I would find that surprising if this was for a geometry or algebra class (or introductory physics) but maybe it would be normal if it's for a camera class.

It's for introductory physics class :D. Ok thanks a lot for your help
 

What is focal length?

Focal length is the distance between the lens of a camera and the image sensor when the subject is in focus. It is usually measured in millimeters (mm).

How does focal length affect image clarity?

The longer the focal length, the narrower the field of view and the larger the subject appears in the image. This can result in a clearer and more detailed image as the subject is magnified.

What is the best focal length for getting a clear image?

The best focal length for getting a clear image depends on various factors such as the type of camera, distance from the subject, and the photographer's intent. Generally, a focal length between 35mm to 50mm is considered best for capturing a clear image without distortion.

Can focal length affect the depth of field?

Yes, focal length can affect the depth of field in an image. A longer focal length tends to have a shallower depth of field, meaning that only a small area of the image is in focus while the rest is blurred. This can be used creatively to isolate a subject or create a dreamy effect in photography.

How does focal length differ in different types of lenses?

Focal length can vary greatly between different types of lenses such as prime lenses, zoom lenses, and telephoto lenses. Prime lenses have a fixed focal length, while zoom lenses have a range of focal lengths. Telephoto lenses have longer focal lengths and are often used for capturing distant subjects.

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