Reflection, Refraction and Lenses: Physics 0625 (Cambridge O Level / IGCSE)

A school astronomy club clamps a laser pointer so that its beam strikes a small plane mirror mounted on a wall bracket. The beam hits the mirror at an angle of incidence of $35°$ to the normal. What is the angle between the incident ray and the reflected ray?

A dance studio has a large vertical plane mirror fixed to one wall so that dancers can check their posture during rehearsals.

(a) State three characteristics of the image of a dancer formed in the plane mirror. [3]

(b) One dancer stands close to the mirror, while a second dancer stands further away, on the same side of the mirror. State how the distance of each dancer's image behind the mirror compares with the distance of that dancer in front of the mirror. [2]

(c) One of the dancers wears a T-shirt with the word "DANCE" printed on the front, facing the mirror. State how this word would appear in the dancer's image, and name the property of the image that explains this. [2]

An optical engineer is designing a small glass sensor that will detect the fuel level inside a car's fuel tank. Before building the sensor, she first tests how the glass bends light by shining a laser beam from air into the flat side of a rectangular block cut from the same glass.

(a) State whether the light ray bends towards or away from the normal as it enters the glass block from air, and explain this in terms of the speed of light in each material. [2]

(b) State what is meant by the critical angle for a ray of light travelling inside the glass towards a glass–air boundary. [1]

(c) State the name of the effect that occurs at a glass–air boundary when the angle of incidence inside the glass exceeds the critical angle, and state what happens to the light ray in this case. [2]

(d) The engineer now builds the sensor: a small glass prism is fixed with its tip pointing down into the fuel tank. A beam of light is shone into the prism so that it strikes the sloped inside surface of the tip at a fixed angle of incidence of $45°$. The critical angle for the glass–air boundary is $40°$, and the critical angle for the glass–fuel boundary is $50°$. Use these values to explain why a detector receives a strong reflected signal when the tip is surrounded by air, but a much weaker signal when the tip is submerged in fuel. [3]

A gemologist is testing an unmounted, transparent stone to check whether it is a genuine diamond or a glass imitation. She shines a laser beam from air onto the flat top face of the stone. The beam strikes the surface at an angle of incidence of $45°$ to the normal, and refracts to an angle of refraction of $30°$ inside the stone.

(a) Calculate the refractive index of the stone. [2]

(b) A genuine diamond has a refractive index of about $2.42$, while ordinary glass has a refractive index of about $1.5$. Using your answer to (a), state and explain whether the stone is more likely to be a genuine diamond or a glass imitation. [2]

(c) Calculate the critical angle for light travelling from inside this stone into air. [2]

(d) Inside the stone, the refracted ray next strikes another internal face at an angle of incidence of $50°$ to the normal. State and explain whether the ray undergoes total internal reflection at this face. [2]

A collector uses a converging lens as a magnifying glass to examine the fine engraving on an antique pocket watch. The lens has a principal focal length of $12\text{ cm}$. The collector holds the lens so that the watch face is $8\text{ cm}$ from the lens, closer to the lens than the principal focal length, and looks through the lens from the other side.

(a) Explain why the watch face must be placed closer to the lens than the principal focal length for the lens to work as a magnifying glass. [2]

(b) Describe how you would construct a ray diagram to locate the image of a point on the watch face, using two rays whose paths through a converging lens are known, and state where the image is formed relative to the lens and the watch face. [3]

(c) State three characteristics of the image seen by the collector. [3]

A diver's underwater torch shines a narrow beam of light upwards through the water towards the flat surface of a swimming pool. The beam strikes the water–air boundary from below at an angle of incidence of $25°$ to the normal, and some of the light passes out into the air above. What happens to the ray as it crosses from the water into the air, and why?

A restorer is repairing a thick rectangular glass panel salvaged from an old ship's porthole. To check that the panel's two flat faces are still exactly parallel to each other, she shines a laser beam from air onto the front face at a fixed angle of incidence of $50°$ to the normal, and tracks the beam as it passes through the glass and out through the back face. The refractive index of the glass is $1.50$.

(a) State the direction in which the ray bends as it enters the glass panel from air, and explain this in terms of the speed of light in each material. [2]

(b) Calculate the angle of refraction inside the glass at the front face. [2]

(c) State the angle of incidence, inside the glass, at which the ray strikes the back face, and explain why this angle equals your answer to (b). [2]

(d) Calculate the angle at which the ray emerges from the back face into the air, and use your answer to explain what this shows about the two faces of the panel. [2]

A doctor uses an endoscope to examine the inside of a patient's stomach. Light travels along a thin, flexible optical fibre inside the endoscope, repeatedly striking the boundary between the fibre's core and its surrounding cladding. At this boundary, the refractive index of the core relative to the cladding is $1.50$.

(a) Calculate the critical angle for light travelling inside the fibre core towards the boundary with the cladding. [2]

(b) A ray of light inside the fibre strikes the core–cladding boundary at an angle of incidence of $55°$ to the normal. State and explain whether total internal reflection occurs at this point. [2]

(c) Explain why it is essential that light continues to strike the sides of the fibre at an angle greater than the critical angle along the entire length of the fibre, and describe what would happen to the light signal at any point where the fibre was bent so sharply that this condition was no longer met. [3]

(d) State one everyday application of optical fibres, other than endoscopes, that relies on total internal reflection. [1]

A ray of light travelling in air strikes the flat surface of a transparent plastic block at an angle of incidence of $60°$ to the normal. The refractive index of the plastic is $1.60$. What is the angle of refraction of the ray inside the plastic block?

A submarine periscope consists of a straight, vertical tube with two identical small plane mirrors fixed inside it (one near the top, one near the bottom) each mirror tilted at $45°$ to the vertical tube. A horizontal ray of light from a ship on the surface enters the periscope through a small opening and strikes the top mirror.

(a) State the angle of incidence of the horizontal ray at the top mirror, measured from the normal to the mirror, and state the angle through which the ray is turned by this one reflection. [2]

(b) The vertical distance between the top and bottom mirrors is $1.2\text{ m}$. Describe the path taken by the reflected ray as it travels from the top mirror down to the bottom mirror. [1]

(c) State the angle of incidence of the ray at the bottom mirror, and describe the direction in which the ray travels after reflecting from this second mirror. [2]

(d) State two characteristics of the final image seen by the periscope operator, as compared with looking directly at the ship with the naked eye (there is no magnification). [2]