Optics Answers

A body A of mass m1 = 5 kg moving along a directed axis in the positive sense with a velocity of 15 m/s collides head-on with a body B of mass m2 = 8 kg moving in the negative sense with a velocity of 4 m/s. If the velocity of m1 after the collision is 4m/s in the negative sense. Apply your scientific knowledge and understanding of impulse and momentum theorem to find the final velocity of m2

A box experienced a force of 200 N East for 8.7 s. Calculate the impulse caused by the force.

Light from a burning match propagates from left to right, first through a thin lens of focal length 5.1 cm, and then through another thin lens, with a 9.7-cm focal length. The lenses are fixed 32.8 cm apart. A real image of the flame is formed by the second lens at a distance of 22.6 cm from the lens.
(a) How far from the second lens, in centimeters, is its optical object located?
(b) How far is the burning match from the first lens, in centimeters?

Consider the compound optical system shown in the diagram, where two thin lenses of focal lengths 8.5 cm (left lens) and 5.5 cm (right lens) are separated by a distance 36 cm.
https://usu34ny.theexpertta.com/images/0anvdqz5.vbh.png

(a) If an object is placed a distance do = 16 cm to the left of the first lens (the left one) as shown in the figure, how far to the right of that lens, in centimeters, is the image formed?
(b) What is the magnification of the first lens?
(c) What is the object distance, in centimeters, for the second lens (the right lens)?
What is the image distance, in centimeters, for the second lens?
(e) What is the magnification of the second lens?

Consider the compound optical system shown in the diagram, where two thin lenses of focal lengths 8.5 cm (left lens) and 5.5 cm (right lens) are separated by a distance 36 cm.

A student is getting her picture taken by a digital camera. The student is ho = 1.55 m tall and she stands d0 = 2.25 m in front of the camera lens which has a focal length of f = 0.041 m.

Randomized Variables
ho = 1.55 m
d0 = 2.25 m
f = 0.041 m

(a) Input an expression for the resulting image distance, di.
(b) By evaluating the numerical distance, find out if the image is real or virtual.
(c) Numerically, what is the magnification of the system?
(d) Numerically, what is the image height in meters?

Suppose a book is held 5.8 cm from a 12-cm focal length lens.

(a) Find the magnification of the image of the book.
(b) Find the magnification of the lens when the book is held 8.4 cm from the magnifier.

Fiber optics are an important part of our modern internet. In these fibers, two different glasses are used to confine the light by total internal reflection at the critical angle for the interface between the core (ncore = 1.495 ) and the cladding (ncladding = 1.458). https://usu34ny.theexpertta.com/images/elusvefv.kmu.png

(a) Numerically, what is the largest angle (in degrees) a ray will make with respect to the interface of the fiber θmax, and still experience total internal reflection?
(b) Suppose you wanted the largest angle at which total internal reflection occurred to be θmax = 5 degrees. What index of refraction does the cladding need if the core is unchanged?

You can determine the index of refraction of a substance by measuring its critical angle for total internal reflection.

Randomized Variables
Θc,w = 74.6°

(a) What is the index of refraction of a substance that has a critical angle of 74.6° when submerged in water (with index of refraction 1.333)?
(b) What would the critical angle be for this substance in air?

Light with a wavelength of 493 nm in vacuum travels through a transparent substance.
(a) What is the wavelength, in nanometers, of this light in water, with a refractive index of 1.33?
(b) What is the wavelength, in nanometers, of this light in Plexiglass, with a refractive index of 1.48?
(c) What is the wavelength, in nanometers, of this light in flint glass, with a refractive index of 1.77?