Question

What’s the definition of refractive index in
(I)in snells law

What’s the sign for focal length while doing the power of lens formula
I-Concave lens
2-Convex Lens

Answer 1

What is Snell's Law?

=> Snell's Law is the ratio of sine of angle of incidence to the sine of angle of refraction. This formula is generally used when a wave passes from one isotropic medium to the other.

Formula = n1/n2 = sinθ2/sinθ1

Or

n1 sinθ1 = n2 sinθ2

Now definition of Refractive Index wrt Snell's Law.

=> Refractive Index (n) is the ratio of velocity of light in vacuum (c) to the velocity of light in the given medium (v).

n = c/v

It is also represented by a symbol named meu (μ).

Moving on to the next part of the question.

In the case of convex lens, the focal length lies in the positive direction of x whereas in the case of concave lens it lies in the negative direction of x, therefore Convex Lens has +ve focal length and Concave Lens has -ve focal length.

Answer 2

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Refractive Index :

If $\sf{i}$ is the angle of incidence and r is the angle of refraction, then

$\sf{\dfrac{sin_i}{sin_r}}$ = constant.

This constant is called the refractive index of the second medium with respect to the first medium and is denoted by $\sf{_2_n_1}$.

Thus, $\sf{_2_n_1}$ = $\sf{\dfrac{sin_i}{sin_r}}$

If $\sf{v_1}$ is the velocity of light in the first medium and $\sf{v_2}$ is the velocity of light in the second medium, then

$\sf{_2_n_1}$ = $\sf{\dfrac{v_1}{v_2}}$

Similarly, the refractive index of the first medium with respect to the second medium is given by,

$\sf{_1_n_2}$ = $\sf{\dfrac{v_2}{v_1}}$

If the first medium is vacuum, $\sf{_2_n_1}$ is considered with respect to vacuum. It is called the absolute refractive index of the medium 2 and is denoted by n.

The refractive index of a medium depends on the magnitude of the velocity of light in the medium.

Let's talk about Snell's Law :

The formula used to describe the relationship between the angle of incidence and angle of refraction, when light or other waves passing travel through a interface between two different isotropic media.

FoRmUlA :

$\sf{n_1\:sin\theta_1\:=\:n_2\:sin\theta_2}$

Where,

• $\sf{n_1}$ =incident index
• $\sf{n_2}$ = refracted index
• $\sf{sin\theta_1}$ = incident angle
• $\sf{sin\theta_2 }$= refracted angle

What's the sign for focal length?

So, for concave lens lens the focal length is negative. Since the beam of light travelling parallel to the principal axis seems to diverge from the focus. The focus is called virtual focus and the focal length is therefore taken as negative.

While for the convex the things go other way round. The beam of light travelling parallel to the principal axis actually meets at focus (converge). The focus is called real focus and the focal length is therefore taken as positive.

How to remember which lens has positive focal length and which one has negative focal length?

Here's a trick, you remember the spelling of convex to help you out to decide the focal length power.

So what's the trick.... You just have to consider the 'x' which is at the end of spelling of convex. Flip the 'x' and it becomes '+' which means the focal length of convex lens is positive. And the focal length of concave lens is negative.