Refraction problem, involving mirrors

[aliaze1]

Homework Statement

A tank whose bottom is a mirror is filled with water to a depth of 19.3 cm. A small fish floats motionless 7.50 cm under the surface of the water.

What is the apparent depth of the reflection of the fish in the bottom of the tank when viewed at normal incidence?

Homework Equations

s = (n1/n2) * s'
therefore
s' = s/(n1/n2)

The Attempt at a Solution

I found the apparent depth of the fish to be 5.64 (viewed from the normal). Then i found the apparent depth of the mirror to be 14.5, and then used the property of mirrors (virtual image distance = real distance, s=s')

(14.5-5.64)*2=17.72, incorrect

 

[aliaze1]

nevermind, i got it

i did [[(19.3*2) -7.5] /1.33]

 

[m2003]

I would first confirm that the values given in the problem are accurate and consistent. I would also ensure that the equations and calculations used are appropriate for the problem at hand. In this case, the equation s = (n1/n2) * s' is used for refraction, which involves the bending of light as it passes through different mediums. However, this problem involves mirrors, which use the law of reflection where the angle of incidence equals the angle of reflection. Therefore, the equation used to find the apparent depth of the reflection in the bottom of the tank should be s' = s.

Using this equation, the apparent depth of the fish's reflection would be the same as its actual depth, which is 7.50 cm. This is because the fish is motionless and directly under the surface of the water, so there is no refraction occurring. The apparent depth of the mirror would also be the same as its actual depth, which is 19.3 cm. Therefore, the distance between the apparent depth of the fish's reflection and the apparent depth of the mirror is 19.3 cm - 7.50 cm = 11.8 cm.

In conclusion, the apparent depth of the reflection of the fish in the bottom of the tank when viewed at normal incidence is 7.50 cm. It is important to use the correct equations and concepts when solving problems involving different optical phenomena, such as refraction and reflection.