In a single slit diffraction with $$\displaystyle \lambda =500nm$$ and a lens of diameter 0.1 mm, width of central maxima, obtain on screen at a distance of 1 m will be
Angle subtended by two minima at the slit in a single slit diffraction $$=\alpha=\dfrac{2\lambda}{w}$$
where, $$w$$ is the slit width.
Here the lens' diameter would act as slit width.
The width of central maxima is the distance between the two minima $$=d\alpha$$
where, $$d$$ is the distance between slit and screen $$=1\ m$$
Thus, the width of central maxima $$=10\ mm$$
The box of a pinhole 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:
Light of wavelength $$560\ nm$$ goes through a pinhole of diameter $$0.20\ mm$$ and falls on a wall at a distance of $$2.00\ m$$. What will be the radius of the central bright spot formed on the wall?
A convex lens of diameter $$8.0\ cm$$ is used to focus a parallel beam of light of wavelength $$620\ nm$$. If the light be focused at a distance of $$20\ cm$$ from the lens, what would be the radius of the central bright spot formed?
If in a cinema hall, the distance between the projector and the screen is increased by $$2\%$$ keeping everything else unchanged, then the intensity of illumination on the screen is:
An opaque ball of diameter $$D = 40 mm$$ is placed between a source of light with wavelength $$\lambda = 0.55 \mu m$$ and photographic plate. the distance between the source and the ball is $$ a = 12 m$$ and that between the ball and photographic plate is $$b = 18 m$$ Find: (a) the image dimension $$y'$$ on the plate if the transverse dimension of the source is $$y = 6.0 mm$$ . (b) the minimum height of irregularities, covering the surface of the ball at random, at which the ball obstructs light.
Light with wavelength $$\lambda = 0.50 \mu m$$ falls on a slit of width $$b = 10 \mu m $$ at an angle $${\theta}_{0} = {30}^{o}$$ to its normal. Find the angular position of the minima located on both the sides of the central Fraunhofer maximum.
Calculate the position of the principal planes points of a thick convex-concave glass lens if the curvature radius of the convex surface is equal to $$ R_{1}=10.0 \mathrm{cm} $$ and of the concave surface to $$ R_{2}=5.0 \mathrm{cm} $$ and the lens thickness is $$ d=3.0 \mathrm{cm} . $$
At what thickness will a thick convex-concave glass lens in the air (a) serve as a telescope provided the curvature radius of its convex surface is $$ \Delta R=1.5 \mathrm{cm} $$ greater than that of its concave surface?
At what thickness will a thick convex-concave glass lens in the air (b) have the optical power equal to -1.0 D if the curvature radii of its convex and concave surfaces are equal to 10.0 and $$ 7.5 \mathrm{cm} $$ respectively?
Find the positions of the principal planes, the focal length and the sign of the optical power of a thick convex-concave glass lens (a) whose thickness is equal to $$ d $$ and curvature radii of the surfaces are the same and equal to $$ R $$;