Optics: light refraction in prisms

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SUMMARY

The discussion centers on the analysis of light refraction in prisms, specifically addressing discrepancies between a textbook approximation and a user's detailed method. The user initially questioned their approach, noting a significant difference in results. Feedback indicated that the textbook may have assumed a different orientation of the prism relative to the wall, which was not clearly stated in the problem. Ultimately, the user resolved their confusion regarding the approximation's applicability to their scenario.

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alingy1
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Could you please check the following problem?
The book made an approximation. I didn't in my method. But the difference seems considerable. Did I make a mistake?
 

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Your analysis looks good. I think maybe the textbook was assuming a different relative orientation between the prism and the wall. See attached figure. But the problem statement is not clear on this point.
 

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EDIT: I get it now.
But, would using that approximation be fine for my picture?
 

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