91Ó°ÊÓ

$$ f = \frac{1}{40.0\,\text{D}} = 0.025\,\text{m} = 2.5\,\text{cm} $$ So, the distance between the stamp and the magnifier (focal length) is 2.5 cm. #tag_title#Step 2: Find the angular magnification#tag_content#The angular magnification M of the magnifying glass can be found using the formula: $$ M = 1 + \frac{D}{f} $$ where \(D = 25\,\text{cm}\) is the near point distance (the closest distance without strain that a person can focus on an object). Plug in the values: $$ M = 1 + \frac{25\,\text{cm}}{2.5\,\text{cm}} $$ #tag_title#Step 3: Compute the angular magnification#tag_content#Now, compute the angular magnification: $$ M = 1 + \frac{25\,\text{cm}}{2.5\,\text{cm}} = 1 + 10 = 11 $$ So, the angular magnification is 11 times. #tag_title#Step 4: Find the size of the image formed#tag_content#Using the angular magnification, we can find the size of the image formed by the magnifier using the formula: $$ H_{\text{image}} = M \times H_{\text{object}} $$ where \(H_{\text{image}}\) is the size of the image, \(H_{\text{object}} = 2.5\,\text{mm}\) is the size of the stamp and \(M = 11 \) is the angular magnification. Plug in the values: $$ H_{\text{image}} = 11 \times 2.5\,\text{mm} $$ #tag_title#Step 5: Calculate the size of the image formed#tag_content#Compute the size of the image formed: $$ H_{\text{image}} = 11 \times 2.5\,\text{mm} = 27.5\,\text{mm} $$ The size of the image formed by the magnifier is 27.5 mm.