Optics Answers

Our eyes have to balance between focus and the amount of light. When we’re in a dark space, the slit in our eyes will open up. Using the concept of diffraction, how does this affect the image that we see?

The subject is at a distance of d = 1.8 meters from the lens. Determine the focal length of the lens if the image size is 5 times the size of the subject.

in the fraunhofer diffraction pattern due to a single slit, the intensity of the central spot is maximum. explain on the basis of geometrical considerations.

In the Fraunhofer diffraction pattern due to a single slit, the intensity of the central 

spot is maximum. Explain on the basis of geometrical considerations.

The prism of spectrometer has a refractive angle of 60 degree and is made of glass whoose refractive index for red and violet are 1.514 and 1.530 respectively

Determine the angle of incidence of the light on the prism

In the Fraunhofer diffraction pattern due to a single slit, the intensity of the central

spot is maximum. Explain on the basis of geometrical considerations

1.  If a glass converging lens is placed in water, its focal length in water will be (a) longer, (b) shorter, or (c) the same as in air. Explain.

2.    A flashlight beam strikes the surface of a pane of glass (n = 1.56) at a 67° angle to the normal. What is the angle of refraction?

Use ray diagrams to show that a real image formed by a thin lens is always inverted, whereas a virtual image is always upright if the object is real.

 (a) A 2.40-cm-high insect is 1.30 m from a 135-mm focal-length lens. Where is the image, how high is it, and what type is it? (b) What if f = -135 mm?

For a wave that travels only in directions that have small angles with respect to the optical axis, the general from of the complex field may be approximated by

U(x, y, z) ≈ A(x, y, z)e^jkz

 where A(x, y, z) is a slowly varying function of z

(a) Show that for such a wave the Helmholtz equation can be reduced to ∇t^2 * A + j2k ∂A/∂z = 0

 where ∇t^2 * A = ∂^2/ ∂x62 + ∂^2/ ∂y^2 is the transverse portion of the Laplacian. This equation is known as the paraxial Helmholtz equation.

(b) Show that a solution to this equation is given by A(x, y, z) = A1/q(z) * (e^jk * ((x^2+y^2)/2*q(z)) for any complex q(z) having dq(z)/dz = 1.