light beam shines through air and then strikes a mirror, making an angle theta = 39.0 degrees with respect to the vertical, as shown. The reflected beam then strikes a pane of glass of thickness h = 1.68 cm, located a distance y= 48.5 cm from the mirror, and then exits the glass pane at the bottom, a horizontal distance x cm away from where it struck the mirror. What is the value of x?

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A light beam shines through air and then strikes a mirror, making an angle theta = 39.0 degrees with respect to the vertical, as shown. The reflected beam then strikes a pane of glass of thickness h = 1.68 cm, located a distance y= 48.5 cm from the mirror, and then exits the glass pane at the bottom, a horizontal distance x cm away from where it struck the mirror. What is the value of x?

The diagram illustrates the refraction and reflection process involving a beam of light as it interacts with different media.

### Diagram Explanation:

- **Surface Description**:
  - **Mirror**: Positioned at the top, the mirror reflects the light beam downward into the air.
  - **Air (n=1)**: This region, with a refractive index of 1, lies between the mirror and the glass. It is the medium through which the light travels after being reflected by the mirror.
  - **Glass (n=1.5)**: Located beneath the air, the glass has a refractive index of 1.5. It is the final medium the light enters after passing through the air.

- **Light Path**:
  - The incident light beam initially strikes the mirror at an angle.
  - **Angle of Incidence (θ)**: This angle is formed between the incident light beam and the normal (an imaginary line perpendicular to the surface) at the point of reflection on the mirror.
  - After reflection, the light enters the air with an incident angle and travels downward.
  - Upon reaching the glass, the light beam refracts (changes direction due to the change in medium) and travels through the glass.

- **Geometric Dimensions**:
  - **y**: The vertical distance from the mirror to the interface between the air and glass.
  - **h**: The vertical distance within the glass where the light travels.
  - **x**: The horizontal distance traveled by the light within the air after reflection from the mirror.
  - **k**: The horizontal distance from the point of incidence on the glass to the point directly under the initial incident point on the mirror.

This diagram is useful for understanding concepts of optics, particularly reflection and refraction, and how light behaves differently across various media.
Transcribed Image Text:The diagram illustrates the refraction and reflection process involving a beam of light as it interacts with different media. ### Diagram Explanation: - **Surface Description**: - **Mirror**: Positioned at the top, the mirror reflects the light beam downward into the air. - **Air (n=1)**: This region, with a refractive index of 1, lies between the mirror and the glass. It is the medium through which the light travels after being reflected by the mirror. - **Glass (n=1.5)**: Located beneath the air, the glass has a refractive index of 1.5. It is the final medium the light enters after passing through the air. - **Light Path**: - The incident light beam initially strikes the mirror at an angle. - **Angle of Incidence (θ)**: This angle is formed between the incident light beam and the normal (an imaginary line perpendicular to the surface) at the point of reflection on the mirror. - After reflection, the light enters the air with an incident angle and travels downward. - Upon reaching the glass, the light beam refracts (changes direction due to the change in medium) and travels through the glass. - **Geometric Dimensions**: - **y**: The vertical distance from the mirror to the interface between the air and glass. - **h**: The vertical distance within the glass where the light travels. - **x**: The horizontal distance traveled by the light within the air after reflection from the mirror. - **k**: The horizontal distance from the point of incidence on the glass to the point directly under the initial incident point on the mirror. This diagram is useful for understanding concepts of optics, particularly reflection and refraction, and how light behaves differently across various media.
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