Question 1190967
Here's how to find the image position and size using principal rays for this converging lens scenario:

**1. Key Information**

*   **Object Height (h₀):** 1.5 cm
*   **Object Distance (d₀):** 5.0 cm
*   **Focal Length (f):** 4.0 cm (positive for converging lens)

**2. Lens Equation (for Calculation)**

While we're focusing on principal rays for the diagram, the lens equation helps us calculate precise values to check our ray diagram against.

*   **Lens Equation:** 1/d₀ + 1/dᵢ = 1/f

Let's solve for image distance (dᵢ):

*   1/dᵢ = 1/f - 1/d₀
*   1/dᵢ = 1/4.0 cm - 1/5.0 cm
*   1/dᵢ = 0.25 cm⁻¹ - 0.2 cm⁻¹
*   1/dᵢ = 0.05 cm⁻¹
*   dᵢ = 20.0 cm

**3. Magnification (for Size)**

*   **Magnification (M):** -dᵢ/d₀

Let's calculate:

*   M = -20.0 cm / 5.0 cm
*   M = -4.0

The negative magnification means the image is inverted.

*   **Image Height (hᵢ):** M * h₀
*   hᵢ = -4.0 * 1.5 cm
*   hᵢ = -6.0 cm

**4. Principal Rays for the Diagram**

Here's how to draw the principal rays for a converging lens:

*   **Ray 1: Parallel Ray**
    *   A ray traveling parallel to the principal axis before the lens refracts and passes through the focal point on the *opposite* side of the lens.
*   **Ray 2: Central Ray**
    *   A ray passing through the center of the lens continues in a straight line, undeflected.
*   **Ray 3: Focal Ray**
    *   A ray passing through the focal point on the *same* side of the lens refracts and travels parallel to the principal axis.

**5. Image Formation**

*   The image is formed where the refracted rays intersect. In this case, the rays converge, forming a real image on the opposite side of the lens from the object.

**Summary**

*   **Image Position:** 20.0 cm from the lens (real image).
*   **Image Size:** 6.0 cm tall and inverted.

**Key Points for Your Diagram**

*   The image is real, so it will be on the opposite side of the lens from the object.
*   The image is inverted.
*   The image is larger than the object.
*   Be sure to draw all three principal rays to confirm the image location.