Forming Images with a Plane Mirror

[asianface.]

[SOLVED] Forming Images with a Plane Mirror

Homework Statement

(a) How rapidly does the distance between you and your mirror image decrease if you walk directly toward a mirror with a speed of 4.7 m/s?

(b) Repeat part (a) for the case in which you walk toward a mirror but at an angle of 31° to its normal.

Homework Equations

Don't really know any or I would have the answer.

The Attempt at a Solution

I thought that for part (a) that the velocity would just be the same because if you're approaching a mirror at a certain speed wouldn't the distance between decrease at the same velocity? Is there a concept that I need to know to understand this?

FYI: I have the Physics: Second Edition by James S. Walker. It's edited by Pearson Education and it has a red cover. If someone could just tell me what page to find something to help me with my answer that would be great. If I still don't understand I guess I'll put my questions here.

 

[Dick]

As you walk towards the plane of the mirror your image also appears to approach the plane of the mirror at the same rate, right? It seems to be so in my shaving experience. Though not everybody shaves. Put the two motions together.

 

[asianface.]

Oh, that makes sense. Wow, thanks.

So for part (b), I just did the answer from part (a) multiplied by the cos(31). It works but I don't completely understand why.

 

[Dick]

Same reason. The velocity at which you are approaching the mirror plane is (4.7m/sec)*cos(31). The image is approaching you at the same rate.

 

[asianface.]

Okay, thanks for the help.

I haven't learned this lesson yet but I'm attempting to finish all the homework assigned for it. I'll probably come back when I run into another problem.

Thank you. :]

 

[asianface.]

Homework Statement

Shaving/makeup mirrors typically have one flat and one concave (magnifying) surface. You find that you can project a magnified image of a light bulb onto the wall of your bathroom if you hold the mirror 2.3 m from the bulb and 5.0 m from the wall. (Include the sign of each answer.)

(a) What is the magnification of the image? (Enter a negative value if the image is inverted.)

(b) What is the focal length of the mirror?

Homework Equations

m=-d_i/d_o
1/f=1/d_o+1/d_i

The Attempt at a Solution

For part (a), I tried the magnification equation and got .46 doing 2.3 / 5. What exactly does the 5.0 meters represent in terms of a variable? If someone could answer that question I could probably do part (b).

 

[Einstienear]

As you walk towards the plane of the mirror your image also appears to approach the plane of the mirror at the same rate, right? It seems to be so in my shaving experience. Though not everybody shaves. Put the two motions together.

Ha ha, "shaving"...

your funny Dick.

Einstienear

 

[asianface.]

._______.
Does anyone know how to help me, please?

 

[kdv]

Homework Statement

Shaving/makeup mirrors typically have one flat and one concave (magnifying) surface. You find that you can project a magnified image of a light bulb onto the wall of your bathroom if you hold the mirror 2.3 m from the bulb and 5.0 m from the wall. (Include the sign of each answer.)

(a) What is the magnification of the image? (Enter a negative value if the image is inverted.)

(b) What is the focal length of the mirror?

Homework Equations

m=-d_i/d_o
1/f=1/d_o+1/d_i

The Attempt at a Solution

For part (a), I tried the magnification equation and got .46 doing 2.3 / 5. What exactly does the 5.0 meters represent in terms of a variable? If someone could answer that question I could probably do part (b).

the 5 meters is the distance to the image d_i

 

[asianface.]

Thanks kdv. :]
One last problem and I'm done.

Homework Statement

The rear window in a car is approximately a rectangle, 1.3 m wide and 0.30 m high. The inside rear-view mirror is 0.62 m from the driver's eyes, and 1.39 m from the rear window. What are the minimum dimensions for the rear-view mirror if the driver is to be able to see the entire width and height of the rear window in the mirror without moving her head?

Homework Equations

Googled the problem and came to this thread. Understood how to use the triangle but still got it wrong.
https://www.physicsforums.com/showthread.php?t=163786

The Attempt at a Solution

I've tried using the triangle in the thread from above but I still can't get it right. I'd show you how I got some of my incorrect answers but I don't have my work with me right now.

 

[asianface.]

Figured it out. Here's the equations you use.

\frac{h_i} {h_o} = \frac{d_i} {d_i+d_o}
\frac{w_i} {w_o} = \frac{d_i} {d_i+d_o}

My classmate showed me the equation but I don't understand why it works and neither does she. If anyone could explain it, please do. :]