Physics

At 10:00 .hrs a 1.5- m-long vertical stick in air casts a shadow 1.4 m long. If the same stick is placed at 10:00 hrs in air in a flat bottomed pool of salt water half the height of the stick, how long is the shadow on the floor of the pool? (For this pool, n = 1.58.) I solved for the inc-angle and got 43.025deg. Solved for ref-angle and got 25.58deg. Quite confused on what to do next.

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  1. the shadow's length is related to the angle of refraction and depth.

    tanTheta2=length/depth
    You know in air, the angle of incidence is given by arctanTHETA1=1.4/1.5
    OR THETA1=43.025 degrees as you found.

    Now, to the shadow. find angle of refraction...I wont check your, but assume 25.58

    then length shadow= depth*tan25.58
    and depth is .5 meters. So the length must be from that formula. HOWEVER, that is the length of shadow of the stick above the water. Sunlight also produces a shadown length for the part of the stick under water. If you draw your ray diagrams, you will convince yourself it is connected to the shadow base of the stick above the water, so the entire shadow should be
    1m*tan25.58

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