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CBSE Class 12-science Answered

What is real depth and apparant depth and deravation

Asked by parjapati16062003 | 10 Jan, 2022, 10:12: AM
Expert Answer
Let us consider an object at O inside water as shown in figure. OC is incident ray that is getting refracted at water-air interface
so that refracted ray deflected away from normal as shown in figure. If a person seeing the object through refracted ray , then
the object will appear at A to him as shwn in figure.
 
Angle of incidence i and angle of refraction are marked and are shown in figure.
 
By law of refraction , 
 
begin mathsize 14px style fraction numerator sin left parenthesis i right parenthesis over denominator sin left parenthesis r right parenthesis end fraction space equals space 1 over mu end style
where μ is refractive index of water with respect to air
 
If angles i and r are small , then sine of angles are approximately equal to tangent of angles
 
begin mathsize 14px style fraction numerator sin left parenthesis i right parenthesis over denominator sin left parenthesis r right parenthesis end fraction space equals space fraction numerator tan left parenthesis i right parenthesis over denominator tan left parenthesis r right parenthesis end fraction space equals space fraction numerator B C divided by O B over denominator B C divided by O A end fraction space equals space fraction numerator O A over denominator O B end fraction space equals space 1 over mu end style
Since OA is real depth and OB is apparent depth , then we have
 
begin mathsize 14px style fraction numerator R e a l space d e p t h over denominator A p p a r e n t space d e p t h end fraction space equals space mu end style
Answered by Thiyagarajan K | 10 Jan, 2022, 02:25: PM
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