Wave Optics

Two point white dots are $$1$$ $$mm$$ apart on a black paper. They are viewed by eye of pupil diameter $$3$$ $$mm.$$ Approximately, what is the maximum distance at which these dots can be resolved by the eye? [ Take wavelength of light $$=500$$ $$nm$$ ]

Assuming human pupil to have a radius of $$0.25$$ $$cm$$ and a comfortable viewing distance of $$25$$ $$cm$$, the minimum separation between two objects that human eye can resolve at $$500$$ $$nm$$ wavelength is :

The box of a pin hole camera, of length $$L,$$ has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength $$\lambda$$ the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say $${b_{\min }}$$) when :

Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm. The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year = 9.46 $$\times$$ 10¹⁵ m) of the order of :

A single slit of width b is illuminated by a coherent monochromatic light of wavelength $$\lambda$$. If the second and fourthminima in the diffraction pattern at a distance 1 m from the slit are at 3 cm and 6 cm respectively from the central maximum, what is the width of the central maximum ? (i.e. distance between first minimum on either side of the central maximum)

A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000 $$\mathop A\limits^ \circ$$ and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is :

The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 $$\mu$$m. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young’s fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance? (i.e. distance between the centres of each slit.)

In a double-slit experiment, green light (5303$$\mathop A\limits^ \circ$$) falls on a double slit having a separation of 19.44 $$\mu$$m and awidht of 4.05 $$\mu$$m. The number of bright fringes between the first and the second diffraction minima is :

Calculate the limit of resolution of a telescope objective having a diameter of 200 cm, if it has to detect light of wavelength 500 nm coming from a star :-

Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600nm. coming from a distant object, the limit of resolution of the telescope is close to :-

The value of numerical aperature of the objective lens of a microscope is 1.25. If light of wavelength 5000 $$\mathop A\limits^o$$ is used, the minimum separation between two points, to be seen as distinct, will be :

Visible light of wavelength 6000 $$\times$$ 10⁻⁸ cm falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at 60^o from the central maximum. If the first minimum is produced at $$\theta$$₁, then $$\theta$$₁, is close to :

Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter 0.1 $$\mu$$m. If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that:

With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 $$\mathop A\limits^o$$ is observed at 5896 $$\mathop A\limits^o$$ ?

A single slit of width $a$ is illuminated by a monochromatic light of wavelength $600 \mathrm{~nm}$. The value of ' $a$ ' for which first minimum appears at $\theta=30^{\circ}$ on the screen will be :

A microwave of wavelength $2.0 \mathrm{~cm}$ falls normally on a slit of width $4.0 \mathrm{~cm}$. The angular spread of the central maxima of the diffraction pattern obtained on a screen $1.5 \mathrm{~m}$ away from the slit, will be :

A monochromatic light of wavelength $6000 ~\mathring{A}$ is incident on the single slit of width $0.01 \mathrm{~mm}$. If the diffraction pattern is formed at the focus of the convex lens of focal length $20 \mathrm{~cm}$, the linear width of the central maximum is :

The diffraction pattern of a light of wavelength $$400 \mathrm{~nm}$$ diffracting from a slit of width $$0.2 \mathrm{~mm}$$ is focused on the focal plane of a convex lens of focal length $$100 \mathrm{~cm}$$. The width of the $$1^{\text {st }}$$ secondary maxima will be :

Given below are two statements : Statement I : When the white light passed through a prism, the red light bends lesser than yellow and violet. Statement II : The refractive indices are different for different wavelengths in dispersive medium. In the light of the above statements, chose the correct answer from the options given below :