Math Problem Statement

Using light rays, determine the location of the image for the object shown. State all four image characteristics using LOST.

Solution

This is a ray diagram question asking you to determine the image characteristics using the LOST (Location, Orientation, Size, and Type) method. Here's how we can analyze this step by step:

  1. Identify the type of mirror:
    Based on the drawing, this is a concave mirror (curved inwards), as indicated by the curvature of the reflecting surface.

  2. Ray Diagram: To determine the image characteristics, you need to trace light rays from the object to the mirror. Usually, at least two rays are used:

    • Ray 1 (Parallel Ray): Draw a ray from the top of the object parallel to the principal axis. After reflecting off the mirror, it passes through the focal point.
    • Ray 2 (Through the Focus): Draw a ray from the top of the object passing through the focal point. After reflecting off the mirror, it travels parallel to the principal axis.
  3. Intersection of Reflected Rays: Where the reflected rays meet is where the image forms. If the rays actually meet, the image is real. If they do not meet but appear to diverge from a point, the image is virtual.


Using LOST Characteristics:

For the specific diagram provided:

  1. Location (L): The image's location depends on the position of the object relative to the focal point (F) and center of curvature (C). For this setup:

    • If the object is beyond the center of curvature, the image forms between the focus and center of curvature.
    • If the object is at the center of curvature, the image forms at the center of curvature.
    • If the object is between the focus and center of curvature, the image forms beyond the center of curvature.
  2. Orientation (O): The image is inverted because the rays converge below the principal axis.

  3. Size (S): The image is either magnified or reduced depending on the object’s position:

    • Beyond the center of curvature: Reduced.
    • At the center of curvature: Same size.
    • Between the center and focus: Magnified.
  4. Type (T): The image is real since the rays actually converge.


Would you like me to draw a detailed ray diagram or clarify further?

Relative Questions:

  1. What happens to the image characteristics if the object is placed at the focal point of the mirror?
  2. How does the size of the image compare to the object if it is placed at twice the focal length?
  3. Can you explain why the image orientation is inverted in a concave mirror setup?
  4. What is the difference between real and virtual images in terms of ray behavior?
  5. How does the curvature of the mirror affect the focal point?

Tip:

Always start with clear ray diagrams for mirror problems to visualize how the image forms.

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Math Problem Analysis

Mathematical Concepts

Geometric Optics
Ray Diagrams

Formulas

Mirror Equation: 1/f = 1/do + 1/di
Magnification: m = -di/do

Theorems

Properties of Concave Mirrors

Suitable Grade Level

Grades 9-12