Q: An optical fiber has a core with index of refraction $$n_a = 1.46$$ and cladding with $$n_b = 1.44. $$What is the largest angle $$\theta ($$with respect to the fiber axis) for which light will be totally internally reflected at the core/cladding boundary?

$$\theta = \arccos\left(\dfrac{n_b}{n_a}\right) = \arccos\left(\dfrac{1.44}{1.46}\right) \approx 16.3^\circ$$

Question 1

An optical fiber has a core with index of refraction $$n_a = 1.46$$ and cladding with $$n_b = 1.44. $$What is the largest angle $$	heta ($$with respect to the fiber axis) for which light will be totally internally reflected at the core/cladding boundary?

Accepted Answer

$$	heta = \arccos\left(\dfrac{n_b}{n_a}ight) = \arccos\left(\dfrac{1.44}{1.46}ight) \approx 16.3^\circ$$

Question 2

Which of the following best describes a virtual image formed by a plane mirror?

Accepted Answer

It is formed when light rays appear to diverge from a point, but never actually meet.

Question 3

A 3.0 cm tall statue is placed 24 cm in front of a concave mirror with a radius of curvature of 20 cm. What is the nature of the image?

Accepted Answer

The image is real and inverted.

Question 4

Which equation correctly relates the object distance $$s$$, image distance $$s'$$, and focal length $$f$$ for a thin lens?

Accepted Answer

$$\dfrac{1}{s} + \dfrac{1}{s'} = \dfrac{1}{f}$$

Question 5

A lens has an index of refraction $$n = 1.7$$, a focal length $$f = 12\,\mathrm{cm}$$, and a front surface radius of curvature $$R_1 = 15$$\,\mathrm{cm}$$. What is the radius of curvature R_2$ of the back surface?

Accepted Answer

$$R_2 = -10.2$$\,\mathrm{cm}$$

Question 6

For a converging lens, what is the sign of the focal length $$f$$ and how does it affect image formation?

Accepted Answer

$$f is $$positive; real and inverted images are formed when the object is outside the focal point.

Question 7

A thin lens forms an image of an object 5.0 cm from the lens. The image is 3.0 cm from the lens on the opposite side. What is the focal length of the lens?

Accepted Answer

$$f = \dfrac{1}{\dfrac{1}{5.0} + \dfrac{1}{3.0}} = 1.88\,\mathrm{cm}$$

Question 8

Which of the following statements about diverging lenses is correct?

Accepted Answer

They always produce virtual, upright, and reduced images.

Question 9

A real image can be described as:

Accepted Answer

Formed when actual light rays converge and meet at a point.

Question 10

If the magnification $$m of a $$mirror is negative, what does this indicate about the image?

Accepted Answer

The image is inverted.

Question 11

A camera lens forms a real image of an object. Which of the following is true?

Accepted Answer

The image can be projected onto a screen and is typically inverted.

Question 12

Which of the following best describes the focal point of a diverging lens?

Accepted Answer

It is the point from which parallel incident rays appear to diverge after passing through the lens.

Question 13

A magnifying glass is an example of which type of lens and what kind of image does it produce when the object is inside the focal length?

Accepted Answer

Converging lens; virtual and upright image.

Question 14

Which of the following is the correct thin lens equation for a lens with index of refraction $$n$$, radii of curvature $$R_1$$ and $$R_2$$, and focal length $$f$$?

Accepted Answer

$$\dfrac{1}{f} = (n-1) \left( \dfrac{1}{R_1$} - \dfrac{1}{R_2$} \right)$$

Question 15

A flat mirror produces an image that is:

Accepted Answer

Virtual, upright, and the same size as the object.

Question 16

If an object is placed at the center of curvature of a concave mirror, where will the image be formed?

Accepted Answer

At the center of curvature, real and inverted.

Geometric Optics: Reflection, Refraction, and Lenses

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