A transparent slab of thickness d has a refractive index n(z) that increases with z . Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n1 and n2 (> n1), as shown in the figure. A ray of light is incident with angle θi from medium 1 and emerges in medium 2 with refraction angle θf with a lateral displacement l . Which of the following statement(s) is(are) true?

# A transparent slab of thickness d has a refractive index n(z) that increases with z . Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n1 and n2 (> n1), as shown in the figure. A ray of light is incident with angle ${\mathrm{\theta }}_{\mathrm{i}}$ from medium 1 and emerges in medium 2 with refraction angle $\mathrm{\theta }$f with a lateral displacement $l$ . Which of the following statement(s) is(are) true?

1. A

$l$ is dependent on n(z)

2. B

${\mathrm{n}}_{1}\mathrm{sin}{\mathrm{\theta }}_{\mathrm{i}}=\left({\mathrm{n}}_{2}-{\mathrm{n}}_{1}\right)\mathrm{sin}{\mathrm{\theta }}_{\mathrm{f}}$

3. C

${\mathrm{n}}_{1}\mathrm{sin}{\mathrm{\theta }}_{\mathrm{i}}={\mathrm{n}}_{2}\mathrm{sin}{\mathrm{\theta }}_{\mathrm{f}}$

4. D

$l$ is independent of n2

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

Since refraction occurs at a set of parallel surfaces,  ${\mathrm{n}}_{1}\mathrm{sin}{\mathrm{\theta }}_{\mathrm{i}}={\mathrm{n}}_{2}\mathrm{sin}{\mathrm{\theta }}_{\mathrm{f}}$
The lateral displacement will depend on how the n(z) varies in the medium .

Clearly, $l$ does not depend on n.

## Related content

 Sine and Cosine Waves Zener Diode Hygrometer Half Wave Rectifier Compound Microscope Solar Cooker MCB Difference Between Scalar and Vector Quantity Difference Between Interference and Diffraction Difference Between Heat and Temperature

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)