JEE Mains · Physics · STD 12 - 9. Ray optics and optical instruments
A monochromatic light wave with wavelength \(\lambda_1\) and frequency \(v_1\) in air enters another medium. If the angle of incidence and angle of refraction at the interface are \(45^{\circ}\) and \(30^{\circ}\) respectively, then the wavelength \(\lambda_2\) and frequency \(v_2\) of the refracted wave are :
- A \(\lambda_2=\lambda_1, v_2=\sqrt{2} v_1\)
- B \(\lambda_2=\frac{1}{\sqrt{2}} \lambda_1, v_2=v_1\)
- C \(\lambda_2=\sqrt{2} \lambda_1, v_2=v_1\)
- D \(\lambda_2=\lambda_1, v_2=\frac{1}{\sqrt{2}} v_1\)
Answer & Solution
Correct Answer
(B) \(\lambda_2=\frac{1}{\sqrt{2}} \lambda_1, v_2=v_1\)
Step-by-step Solution
Detailed explanation
Snell's law \(\mu_1 \sin 45^{\circ}=\mu_2 \sin 30^{\circ}\) \(\frac{\mu_1}{\mu_2}=\frac{1}{\sqrt{2}}\) \(\Rightarrow \frac{\mu_1}{\mu_2}=\frac{\lambda_2}{\lambda_1}=\frac{1}{\sqrt{2}}\) \(\Rightarrow \lambda_2=\frac{\lambda_1}{\sqrt{2}}\) Frequency doesn't change on change in…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- Three harmonic waves having equal frequency \(\mathrm{v}\) and same intensity \(\mathrm{I}_{0}\), have phase angles \(0 , \frac{\pi}{4}\) and \(-\frac{\pi}{4}\) respectively. When they are superimposed the intensity of the resultant wave is close toJEE Mains 2020 Medium
- Consider two uniform discs of the same thickness and different radii \(R _{1}= R\) and \(R _{2}=\alpha R\) made of the same material. If the ratio of their moments of inertia \(I_{1}\) and \(I_{2}\), respectively, about their axes is \(I _{1}: I _{2}=1: 16\) then the value of \(\alpha\) isJEE Mains 2020 Hard
- The velocity of the bullet becomes one third after it penetrates \(4\,cm\) in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at \((4+x)\,cm\) inside the block. The value of \(x\) is\(.....\)JEE Mains 2022 Medium
- A microscope was initially placed in air (refractive index \(1)\). It is then immersed in oil (refractive index \(2)\). For a light whose wavelength in air is \(\lambda\), calculate the change of microscope's resolving power due to oil and choose the correct option.JEE Mains 2022 Medium
- A hydraulic press can lift \(100\, kg\) when a mass \('m'\) is placed on the smaller piston. It can lift ......... \(kg\) when the diameter of the larger piston is increased by \(4\) times and that of the smaller piston is decreased by \(4\) times keeping the same mass \('m'\) on the smaller piston.JEE Mains 2021 Hard
- The surface charge density of a thin charged disc of radius \(R\) is \(\sigma \). The value of the electric field at the centre of the disc is \(\frac{\sigma }{{2\,{ \in _0}}}\). With respect to the field at the centre, the electric field along the axis at a distance \(R\) from the centre of the discJEE Mains 2013 Hard
More PYQs from JEE Mains
- An \(\alpha\) particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particals will be.JEE Mains 2022 Medium
- If the matrix \(A=\left(\begin{array}{cc}0 & 2 \\ K & -1\end{array}\right)\) satisfies \(A\left(A^{3}+3 I\right)=2 I\) then the value of \(\mathrm{K}\) is :JEE Mains 2021 Hard
- If speed \((V)\), acceleration \((A)\) and force \((F)\) are considered as fundamental units, the dimension of Young’s modulus will beJEE Mains 2023 Hard
- A magnetic compass needle oscillates \(30\) times per minute at a place where the dip is \(45^o\), and \(40\) times per minute where the dip is \(30^o\). If \(B_1\) and \(B_2\) are respectively the total magnetic field due to the earth at the two places, then the ratio \(B_1/B_2\) is best given byJEE Mains 2019 Medium
- A Carnot engine whose heat \(\operatorname{sinks}\) at \(27\,^{\circ} C\), has an efficiency of \(25 \%\). By how many degrees should the temperature of the source be changed to increase the efficiency by \(100 \%\) of the original efficiency \(?\)JEE Mains 2022 Hard
- A \(16\ \Omega\) wire is bend to form a square loop. A \(9 \mathrm{~V}\) battery with internal resistance \(1\ \Omega\) is connected across one of its sides. If a \(4\ \mu \mathrm{F}\) capacitor is connected across one of its diagonals, the energy stored by the capacitor will be \(\frac{x}{2} \ \mu \mathrm{J}\). where \(x=\) ________.JEE Mains 2024 Hard