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Zorluk: KolayRefraction of Light, Total Internal Reflection, and Prisms

A water tank has a real depth of 16.0 cm16.0\text{ cm}. If the refractive index of water relative to air is 43\frac{4}{3}, what is the apparent depth of the tank in centimetres when viewed normally from above?

Cevap: 12 cm

Cevap

The apparent depth of the water tank is 12.0 cm12.0\text{ cm}.
When light passes from water to air, refraction causes the apparent depth to be smaller than the real depth by a factor equal to the refractive index nn. Substituting a real depth of 16.0 cm16.0\text{ cm} and n=43n = \frac{4}{3} into Apparent Depth=Real Depthn\text{Apparent Depth} = \frac{\text{Real Depth}}{n} yields 12.0 cm12.0\text{ cm}.

Adım Adım Çözüm

1
Identify the relationship between refractive index, real depth, and apparent depth.
n=Real DepthApparent Depthn = \frac{\text{Real Depth}}{\text{Apparent Depth}}
Refraction at a plane boundary causes an object immersed in a denser medium to appear closer to the surface when viewed from a rarer medium.
2
Rearrange the equation to isolate Apparent Depth.
Apparent Depth=Real Depthn\text{Apparent Depth} = \frac{\text{Real Depth}}{n}
The unknown quantity requested by the question is the apparent depth.
3
Substitute the known numerical values into the equation.
Apparent Depth=16.043=16.0×34=12.0 cm\text{Apparent Depth} = \frac{16.0}{\frac{4}{3}} = 16.0 \times \frac{3}{4} = 12.0\text{ cm}
Dividing 16.016.0 by 43\frac{4}{3} gives 12.012.0.

Anahtar Kavram

Real and Apparent Depth in Light Refraction
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Konular

Refraction of Light, Total Internal Reflection, and Prisms

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