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What is the image distance of an object placed 3.00 cm in front of a convex mirror that has a focal length of 8.00 cm? -3.8 cm 7.8 cm O-4.8 cm O-6.8 cm

User Leosan
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2 Answers

4 votes

Final answer:

The image distance for an object placed in front of a convex mirror is calculated using the mirror equation. The image distance found is approximately -2.18 cm, indicating a virtual image behind the mirror.

Step-by-step explanation:

The question involves finding the image distance of an object placed in front of a convex mirror using the mirror equation. The mirror equation for a convex mirror is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. Since the convex mirror has a focal length of 8 cm, and the object distance (do) is 3 cm, we plug these into the equation. Remember that for a convex mirror, the focal length is taken as negative (-8 cm in this case). So, the equation becomes:

1/(-8) = 1/3 + 1/di

This gives us:

-1/8 = 1/3 + 1/di

Bringing 1/3 to the left side, we get:

-1/8 - 1/3 = 1/di

Finding a common denominator, we have:

-3/24 - 8/24 = 1/di

-11/24 = 1/di

Therefore, di = -24/11 cm, which is approximately -2.18 cm.

Since the image distance is negative, this indicates that the image is virtual and is located behind the mirror.

User Fede Mika
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6 votes

Final answer:

The image distance of an object placed 3.00 cm in front of a convex mirror with a focal length of 8.00 cm is -4.8 cm.

Step-by-step explanation:

To find the image distance of an object placed in front of a convex mirror, we can use the mirror equation: 1/f = 1/di + 1/do. In this equation, f is the focal length of the mirror, di is the image distance, and do is the object distance. Given that the object distance is 3.00 cm and the focal length is 8.00 cm, we can plug in the values to find di: 1/8.00 = 1/di + 1/3.00. Solving for di gives us an image distance of -4.8 cm.

User Solujic
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