Choose the letter that best answers the question or complete s the statement. When a ray strikes a plane mirror at an angle, (A) the light ray slows down and bends. (B) an inverted virtual image is formed. (C) the light ray is refracted. (D) the angle of incidence of the ray equals the angle of reflection of the ray. (E) the image formed is real.

A He-Ne gas laser which produces monochromatic light of wavelength $\lambda=6.328 \times 10^{-7} \mathrm{~m}$ is used to calibrate a reflection grating in a spectroscope. The first-order diffraction line is found at an angle of $18.5^{\circ}$ to the incident beam. How many lines per meter are imprinted on this reflecting diffraction grating?

Explain how translations, reflections, and rotations affect the size and shape of an image. Justify.

Interpret each equation as indicating: The reflection image of point ____ over ____ is the point ____.

$$\left[\begin{array}{rr} 0 & -1 \\ -1 & 0 \end{array}\right]\left[\begin{array}{l} 4 \\ 4 \end{array}\right]=\left[\begin{array}{l} -4 \\ -4 \end{array}\right]$$

A string has an abrupt change in linear density at its midpoint so that the speed of a pulse on the left side is 2/3 of that on the right side. a. On which side is the linear density greater? Explain. b. From which side would you start a pulse so that its reflection from the midpoint would not be inverted? Explain.

If $A^{\prime}, B^{\prime}, C^{\prime}$, and $D^{\prime}$ are the images of any four points $A, B, C$, and $D$, then we say the ratio of distances is invariant under the transformation if $\frac{A B}{C D}=\frac{A^{\prime} B^{\prime}}{C^{\prime} D^{\prime}}$. For which of the following transformations is the ratio of distances invariant? a. reflection b. rotation c. dilation

For this item, Filip claims triangle N'P'Q' is a reflection of triangle NPQ over the x-axis. Is Filip correct? Justify your answer.

Given: Plot triangle NPQ with vertices N(-3,1), P(-1,3), and Q(1,2). The coordinates of the vertices of $\triangle N^{\prime} P^{\prime} Q^{\prime}$ are $N^{\prime}$(-3,-3), $P^{\prime}$(-1,-5), and $Q^{\prime}$(1,-4)

(a) Find the vector equation describing the reflection of r in a plane whose unit normal is n. (b) Show that if $l_{i}$, i = 1, 2, 3, are the direction cosines of n, then the matrix of transformation has the elements

$$A_{i j}=\delta_{i j}-2 l_{i} l_{j}$$

and verify that A is an improper orthogonal matrix.

The vertices of rectangle NOPQ are N(8, 8), O(8, 2), P(-3, 2), and Q(-3, 8). Describe the reflection used to form each rectangle. Explain your reasoning. a. N'(-8, 8), O'(-8, 2) P'(3, 2), and Q'(3, 8). b. N"(8, -8), O"(8, -2), P"(-3, -2), and Q"(-3, -8).

A point undergoes a reflection across the $x$-axis, but stays in the same location. a. Find two different scts of coordinates that the point might have. b. Make a conjecture about which points stay in the same place when reflected across the $x$-axis. c. Use the coordinate definition of a rellection across the $x$-axis to justify your conjecture in part b.

Which parameters can cause the graph of a power function to be reflected? Describe the type of reflections.

A particle of mass m and energy E moving in a region where there is initially no potential energy encounters a potential dip of width L and depth $U = -U_0.$ Show that the reflection probability is given by

$$U(x)=\left\{\begin{array}{cc}{0} & {x \leq 0} \\ {-U_{0}} & {0<x<L} \\ {0} & {x \geq L}\end{array}\right.$$

Describe a sequence of translations, reflections, or rotations that would transform figure J into figure K.

The vertices of

$$\Delta L M N$$

are L(-2, 4), M(1, 2), and N(-3, -5). Suppose j is a line with equation x = 3 and k is a line with equation y = -2. What are the coordinates of the vertices of

$$\Delta L ^ { \prime } M ^ { \prime } N ^ { \prime }$$

for each glide reflection?

$$T _ { \langle 2, -3 \rangle} \circ R _ { k }$$