# Speed of image refracted from an object in motion in another medium

There are two ways of approaching this question according to me

1. Relation between speed of light in a medium and refractive index of the medium.

$$C \alpha \frac{1}{n}$$

$$C$$ - speed of light in a medium

$$n$$ - refractive index of the medium

So $$\frac{C_1}{C_2}=\frac{n_2}{n_1}$$

From the question we find the velocity of object in air (which we get as $$12 ms^{-1})$$, and put it in this equation. I’m not sure if we can use this one since it’s for speed of light, but intuitively it feels right.

1. Differentiating the relation between apparent depth and real depth to get velocity.

$$\frac{d_0}{d}=\frac{n_2}{n_1}$$

$$\frac{V_0}{V}=\frac{n_2}{n_1}$$

$$d_0$$ - apparent depth

$$d$$ - real depth

$$V_0$$ - apparent velocity

$$V$$ - real velocity

The correct answer is obtained when the second method is used. But I’m not so convinced as to why the first one can’t be used. Can you give me example to prove why that way is wrong or implications of the assumption that I’ve taken while solving with method 1?

I mean if light emitted by an object(which moves with some velocity) goes to another medium with faster/slower velocity which then decides the velocity of image. We should be able to use the relation mentioned in method 1, right?

Can you give me example to prove why that way is wrong or implications of the assumption that I’ve taken while solving with method 1

In the first formula , you can replace C with $$\nu \lambda$$ , where $$\nu$$ = frequency of light (which is source dependent) and $$\lambda$$ is the wavelength of the light (depends on the medium). Both of these quantities have nothing to do with the speed of the object.