91Ó°ÊÓ

#tag_title# Step 3: Calculate the image distance (d_i) #tag_content#Using the lens formula, we can find the image distance: \(\frac{1}{d_i} = \frac{1}{12} - \frac{1}{10}\) Now, we calculate the common denominator and subtract the fractions: \(\frac{1}{d_i} = \frac{10 - 12}{120}\) \(\frac{1}{d_i} = -\frac{2}{120}\) Now, we take the reciprocal to find d_i: \(d_i = -60\) cm The negative sign indicates that the image is on the same side of the lens as the object, which means it is a virtual image. #tag_title# Step 4: Calculate the magnification #tag_content#Magnification (m) is given by the ratio of the image distance to the object distance: \(m = \frac{d_i}{d_o}\) Using the given values, we can calculate the magnification: \(m = \frac{-60}{10}\) \(m = -6\) The negative magnification indicates that the image is inverted relative to the object. #tag_title# Step 5: Calculate the image height #tag_content#Now, we can find the image height (h_i) using the magnification: \(h_i = m \times h_o\) We already know the magnification and object height: \(h_i = -6 \times 5.00\) mm \(h_i = -30.0\) mm The image is 30.0 mm tall and inverted. #tag_title# Step 6: Determine the properties of the image #tag_content#The image properties can be summarized as follows: - Position: The image is 60 cm from the lens on the same side as the object (virtual image). - Magnification: The image is 6 times larger than the object (magnification of -6). - Orientation: The image is inverted, as indicated by the negative magnification. - Size: The image height is 30.0 mm. #tag_title# Step 7: Calculate the angular magnification #tag_content#Angular magnification (M) is given by the ratio of the image size to the object size: \(M = -m\) Using the magnification we obtained earlier: \(M = -(-6)\) \(M = 6\) Therefore, the angular magnification is 6. #tag_title# Short Answer #tag_content#The image of the insect is 60 cm away on the same side of the lens as the object, forming a virtual image. The image is 30.0 mm tall, which is 6 times larger than the object, and it is inverted. The angular magnification is 6.