Geometrical Optics Questions and Answers

A certain digital camera having a lens with focal length 7.50 cm focuses on an object 1.75 m tall that is 4.70 m from the lens. A How far must the lens be from the sensor array?

The glass core of an optical fiber has an index of refraction 1.60. The index of refraction of the cladding is 1.50. What is the maximum angle a light ray can make with the wall of the core if it is to remain inside the fiber?

An object is 13 cm in front of a diverging lens with a focal length of -7 cm. You may want to review (Pages 973-978). Determine the location of the image. Express your answer to two significant figures and include the appropriate units. Is the image upright or inverted?

The two mirrors in the figure below meet at a right angle. The beam of light in the vertical plane P strikes mirror 1 at 0, 42.2 as shown. (a) Determine the distance the reflected light beam travels before striking mirror 2. (b) In what direction does the light beam travel after being reflected from mirror 27

A violet ray of light leaves a medium with refractive index of 26.92 and enters a second medium with refractive index of 11.11 at an angle of 0.64 radians to the normal. At what angle to the normal was this ray traveling in the first medium? a. 0.4981 radians b. 0.9115 radians c. 0.0027 radians d. 0.0249 radians e. 0.1245 radians f. 0.2490 radians

a) Suppose that in an imaging system using a lens the focal length of the lens is 4cm and the image plane is a distance 8cm behind the lens. How far in front of the lens on the optical axis of the system must we place a point to get a perfect image of the point? b) If the lens diameter is 1cm and a point is placed at 10cm in front of the lens, what will be the diameter of the image of the point?

A narrow beam of light is incident at the origin at angle i = 30° as shown in figure. The refractive index is function of y in region y 20 according to function μ =1/√1+y^2 coordinate where the beam can reach : √2 2 √3 3

Suppose that you have a magnifying glass which you hold at arm's length to look at some text on a nearby poster. (a) Describe the features of the image you see - specifically, is it real or virtual? Upright or inverted? Enlarged, reduced, or the same size? (b) Explain how the image would change if you took two steps away from the poster, still looking at it through the magnifying glass at arm's length.

As shown in the figure, a ray of light strikes a plane mirror with some incident angle. The mirror is now rotated by an angle of α = 16.0° about an axis through the point where N₁ contacts the mirror, without altering the incident ray. The new position is shown by the line M₂. (a) Determine the angle through which the reflected ray rotates if the incident angle is 40.0°. (b) Determine the angle through which the reflected ray rotates if the incident angle is 50.0⁰.

We know that the index of refraction of materials can help identify those materials. A light beam is shined onto a surface a reflected ray and is found to be completely polarized when the angle of incidence is 61.0⁰. (a) What is the index of refraction of the reflecting material? (b) What is the angle of refraction if some light passes through the surface of the material?

A clear plastic paperweight with an unknown index of refraction rests on your desk as shown in the figure. A ray of light enters the top of the paper weight with a 59° angle of incidence and undergoes total internal reflection at the side. (a) Determine the minimum value for the index of refraction of the plastic for which this will occur. (b) If the angle of incidence as the light enters the paper weight is increased, is the minimum value for the index of refraction increased or decreased?

As shown in the figure, a light beam travels from air, through olive oil, and then into water. If the angle of refraction 02 for the light in the olive oil is 34.4°, determine the angle of incidence ₁ in air and the angle of refraction 03 in water. The index of refraction for olive oil is 1.47.

The equation connecting s, p, and f for a simple lens can be employed for spherical mirrors, too. A concave mirror with a focal length of 9 cm forms an image of a small object placed 15 cm in front of the mirror. Where will this image be located? (For spherical mirrors, positive p means the image is on the same side of the mirror as the object.)

A 1.2 cm-tall object stands in front of a converging lens. It is desired that a virtual image 2.1 times larger than the object be formed by the lens. How far from the lens (in cm) must the object be placed to accomplish this task, if the final image is located 18 cm from the lens?

You can determine the index of refraction of a substance by determining its critical angle. (a) What is the index of refraction of a substance that has a critical angle of 49.7° when submerged in ethanol, which has an index of refraction of 1.361? (b) What would the critical angle be for this substance in air?

The focal length of a diverging lens is negative. If f = -11 cm for a particular diverging lens, where will the image be formed of an object located 31 cm to the left of the lens on the optical axis? cm to the left of the lens What is the magnification of the image?

A glass block with index of refraction n = 1.7 is immersed in an unknown liquid. A red beam of light traveling in the glass is incident on the top of the block. As shown in the diagram, there is no refracted ray. a) Is the index of refraction of the liquid ny larger than, smaller than, or equal to the index of refraction of the block? Explain your reasoning. b) Determine an inequality for the index of refraction n (this should be a pure number). Explain why this is an inequality instead of an equality.

An object (represented by an arrow) is placed 6 cm from a diverging lens, as shown in the diagram below. At this location, the object makes a virtual image that is 1/3 the size of the object. a) Determine the image distance d; (both sign and value). Show your work and explain your reasoning. b) Determine the focal length of the lens. Then complete the ray diagram by indicating the focus and drawing the two principal rays that show how the image is formed by the object. Show your work and explain your reasoning.

An object is placed 5 cm from a diverging lens with a focal length of 3 cm. a) [1.5 points] Complete the ray diagram below to determine the location of the image using at least two principal rays. Summarize the characteristics of the image (real/virtual, upright/inverted, larger/smaller/same size) from your diagram. Explain what these characteristics tell us about the signs of the image distance (d;) and image height (h₁). b) Calculate the height of the image (hi) and its distance from the center of the lens (di). Show your work and note whether your results are consistent with your diagram above. c) What is the magnification of the image (both sign and value)? How does the magnification tell you about the characteristics of the image? Show your work and explain. d) How could you move the object such that the magnification is -2/3, rather than the value you calculated above? If this is not possible, state so explicitly. Explain.

A dentist uses a mirror to examine a tooth that is 1.00 cm in front of the mirror. The image of the tooth is formed 10.0 cm behind the mirror. Determine the magnification of the image, M, and focal point, f. [Hint: Positive focal point is for a concave mirror, negative for convex.]

A ray of green light struck a glass slab (with the index of refraction 1.52) at 30 degrees to the normal. Find the angle between reflected and refracted light. in degrees, 2 significant figure

A ray of green light traveling in a glass slab (with the index of refraction 1.67) strikes the interface with the air at 30 degrees to the normal. Find the critical angle of total internal reflection and conclude if the light would refract out to the air. in degrees, 2 significant figures A. 36.8, will not refract out, totally internally reflect B. 53.2, will not refract out, totally internally reflect C. 53.2, will refract out D. 36.8, will refract out

Two mirrors are arranged at 110 degrees. If the light strikes the surface of the first mirror at 50 degrees to the normal and the reflected ray strikes the second mirror, what is the angle between the direction of incident and doubly reflected ray. in degrees, 2 significant figures