Question

An object is placed 8 cm in front of a convex lens of focal length 6 cm. Find the image location by drawing a ray tracing diagram to scale. Verify your answer using the lens equation.

Answer 1

Answer on Question 48661, Physics, Optics

Question:

An object is placed $8\mathrm{cm}$ in front of a convex lens of focal length $6\mathrm{cm}$ . Find the image location by drawing a ray tracing diagram to scale. Verify your answer using the lens equation.

Answer:

Let's draw a ray tracing diagram:

Let's the scale will be equals to focal length $6\mathrm{cm}$ , for convenience. So, we can see from the ray tracing diagram that rays from the object after its passes the lens, intersects and forms a real image. Also, we can see that the distance from the lens to the image $d_{i}$ is equals four focal length, that is $24\mathrm{cm}$ . So let's verify the answer by using the lens equation:

$$\frac {1}{d _ {o}} + \frac {1}{d _ {i}} = \frac {1}{f},$$

where $d_{o}$ is the distance from object to the lens, $d_{i}$ is the distance from the lens to the image and $f$ is the focal length. Substituting $d_{o}$ and $f$ from the condition of the problem we have:

$$\frac {1}{8 c m} + \frac {1}{d _ {i}} = \frac {1}{6 c m},$$

From this expression we obtain $d_{i} = 24cm$ . Distance from the lens to the image is positive, so image is real. Therefore, we find the image location correctly.

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