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You may use a calculator. An object is placed 10.0 cm to the left of a convex lens with a focal length of +8.0 cm. Where is the image of the object? O 40 cm to the left of the lens O 18 cm to the right of the lens 40 cm to the right of the lens O 18 cm to the left of the lens

You may use a calculator. An object is placed 10.0 cm to the left of a convex lens with a focal length of +8.0 cm. Where is the image of the object? O 40 cm to the left of the lens O 18 cm to the right of the lens 40 cm to the right of the lens O 18 cm to the left of the lens

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**Physics Practice Problem: Convex Lens** *You may use a calculator.* --- **Problem Statement:** An object is placed 10.0 cm to the left of a convex lens with a focal length of +8.0 cm. Where is the image of the object? **Options:** - ⓞ 40 cm to the left of the lens - ⓞ 18 cm to the right of the lens - ⓞ 40 cm to the right of the lens - ⓞ 18 cm to the left of the lens --- **Analysis:** To solve this problem, we use the lens formula: \[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \] where: - \( f \) is the focal length of the lens (\(+8.0 \, \text{cm}\)) - \( d_o \) is the object distance ( \(-10.0 \, \text{cm}\), negative because it is to the left and conventionally considered negative for convex lens formula) - \( d_i \) is the image distance to be calculated. By substituting the values into the lens formula, we can solve for \( d_i \). \[ \frac{1}{8} = \frac{1}{-10} + \frac{1}{d_i} \] \[ \frac{1}{d_i} = \frac{1}{8} - \frac{1}{10} \] \[ \frac{1}{d_i} = \frac{10 - 8}{80} \] \[ \frac{1}{d_i} = \frac{2}{80} \] \[ d_i = \frac{80}{2} \] \[ d_i = 40 \, \text{cm} \] So, the image is located **40 cm to the right of the lens**. Thus, the correct option is: - ⓞ 40 cm to the left of the lens - ⓞ 18 cm to the right of the lens - ⓞ **40 cm to the right of the lens** - ⓞ 18 cm to the left of the lens
Transcribed Image Text:**Physics Practice Problem: Convex Lens** *You may use a calculator.* --- **Problem Statement:** An object is placed 10.0 cm to the left of a convex lens with a focal length of +8.0 cm. Where is the image of the object? **Options:** - ⓞ 40 cm to the left of the lens - ⓞ 18 cm to the right of the lens - ⓞ 40 cm to the right of the lens - ⓞ 18 cm to the left of the lens --- **Analysis:** To solve this problem, we use the lens formula: \[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \] where: - \( f \) is the focal length of the lens (\(+8.0 \, \text{cm}\)) - \( d_o \) is the object distance ( \(-10.0 \, \text{cm}\), negative because it is to the left and conventionally considered negative for convex lens formula) - \( d_i \) is the image distance to be calculated. By substituting the values into the lens formula, we can solve for \( d_i \). \[ \frac{1}{8} = \frac{1}{-10} + \frac{1}{d_i} \] \[ \frac{1}{d_i} = \frac{1}{8} - \frac{1}{10} \] \[ \frac{1}{d_i} = \frac{10 - 8}{80} \] \[ \frac{1}{d_i} = \frac{2}{80} \] \[ d_i = \frac{80}{2} \] \[ d_i = 40 \, \text{cm} \] So, the image is located **40 cm to the right of the lens**. Thus, the correct option is: - ⓞ 40 cm to the left of the lens - ⓞ 18 cm to the right of the lens - ⓞ **40 cm to the right of the lens** - ⓞ 18 cm to the left of the lens
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