Image distance after passing through lens and mirror

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The discussion revolves around calculating image distances after light passes through a lens and reflects off a mirror. The lens has a positive focal length of +77.9 cm, while the mirror has a negative focal length of -59.0 cm, with a separation distance of 1.00 m. The user initially misapplied the lens formula and incorrectly interpreted the image's position relative to the mirror. Clarifications were provided regarding the virtual image created by the mirror and the correct application of the lens formula. Ultimately, the user acknowledged a mistake in their calculations and received assistance in verifying their work.
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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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Post your working here and we'll help you find your mistakes, yeah? We don't provide full solutions here at PF. :)
 
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.
 
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.
 
you were right! thank you so much
 
Dhananjay97 said:
you were right! thank you so much

Yup, it's my pleasure! :smile:
 

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