Image distance after passing through lens and mirror

In summary, the lens and mirror in the figure below are separated by d = 1.00 m and have focal lengths of +77.9 cm and -59.0 cm, respectively. An object is placed p = 1.00 m to the left of the lens as shown. Assuming that the image from the mirror goes through the mirror again, the object distance is found to be -76.9907 cm which puts the image to the right of the mirror.
  • #1
Dhananjay97
3
0
Member warned about proper use of the template and showing an attempt at solution.
36-p-063.gif
The lens and mirror in the figure below are separated by d = 1.00 m and have focal lengths of +77.9 cm and -59.0 cm, respectively. An object is placed p = 1.00 m to the left of the lens as shown. i need to find the final object distance and have no idea what am i doing wrong. I am just using the equation 1/f=1/p+1/q over and over again but the answer is always wrong
 
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  • #2
Post your working here and we'll help you find your mistakes, yeah? We don't provide full solutions here at PF. :)
 
  • #3
first i started with the object and the lens and substituted the values in the equation 1/f=1/q+1/p since we know focal length of the lens and the object distance, and got 352.489 cm. This put the image to the right side of the mirror. Now the object of the mirror (the image of the lens) is on the same side as the focal point of the mirror so I solved for q again using the same equation and using -252.489 cm as my p (subtracted 100 cm because that was the distance between the lens and mirror). i got - 76.9907cm which meant the image was still to the right of the mirror. from there i followed two approaches:-
1) assume that the image from the image goes straight to the lens and use -176.9907 cm as p to solve for q to get 38.72 cm to the left of the lens
2) assume that the image from the mirror goes through the mirror again solve for the mirror again, using the same equation but the image kept going further to the right.
 
  • #4
Dhananjay97 said:
2) assume that the image from the mirror goes through the mirror again solve for the mirror again, using the same equation but the image kept going further to the right.

This approach is incorrect. The light ray has already reflected off the mirror at that point, and is going towards the lens. It just appears to be coming from behind the mirror (virtual image).

Dhananjay97 said:
1) assume that the image from the image goes straight to the lens and use -176.9907 cm as p to solve for q to get 38.72 cm to the left of the lens

Check your working for this step again. I suspect you might have a careless mistake here.
 
  • #5
you were right! thank you so much
 
  • #6
Dhananjay97 said:
you were right! thank you so much

Yup, it's my pleasure! :smile:
 

Related to Image distance after passing through lens and mirror

1. What is the difference between the image distance after passing through a lens and a mirror?

The main difference between the image distance after passing through a lens and a mirror is that the image distance through a lens is always positive, while the image distance through a mirror can be either positive or negative. This is due to the way lenses and mirrors refract and reflect light, resulting in different image formation processes.

2. How does the focal length of a lens affect the image distance?

The focal length of a lens directly affects the image distance, as it determines the amount of refraction that occurs when light passes through the lens. A shorter focal length will result in a shorter image distance, while a longer focal length will result in a longer image distance.

3. Can the image distance be greater than the object distance?

Yes, the image distance can be greater than the object distance. This occurs when the object is placed between the focal point and the lens/mirror. In this case, the image distance will be positive and the image will be formed on the same side of the lens/mirror as the object.

4. How does the position of the object affect the image distance?

The position of the object relative to the lens/mirror has a significant impact on the image distance. If the object is placed closer to the lens/mirror, the resulting image will be further away and have a longer image distance. Conversely, if the object is placed further away, the image will be closer and have a shorter image distance.

5. What is the formula for calculating the image distance after passing through a lens/mirror?

The formula for calculating the image distance after passing through a lens/mirror is given by: 1/image distance = (1/focal length) - (1/object distance), where the focal length is the distance from the lens/mirror to the point where parallel light rays converge, and the object distance is the distance from the lens/mirror to the object. This formula is known as the thin lens/mirror equation.

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