A diverging lens has a focal length of magnitude 15.8 cm. (a) Locate the images

Question

A diverging lens has a focal length of magnitude 15.8 cm. (a) Locate the images for each of the following object distances. 31.6 cm distance cm location 15.8 cm distance cm location 7.9 cm distance cm location (b) Is the image for the object at distance 31.6 real or virtual? real virtual Is the image for the object at distance 15.8 real or virtual? real virtual Is the image for the object at distance 7.9 real or virtual? real virtual (c) Is the image for the object at distance 31.6 upright or inverted? upright inverted Is the image for the object at distance 15.8 upright or inverted? upright inverted Is the image for the object at distance 7.9 upright or inverted? upright inverted (d) Find the magnification for the object at distance 31.6 cm. Find the magnification for the object at distance 15.8 cm. Find the magnification for the object at distance 7.9 cm.

A diverging lens has a focal length of magnitude 15.8 cm (a) Locate the images for each of the following object distances 31.6 cm distance location Select- - cm 15.8 cm distance location Select- - cm 7.9 cm distance location Select- - cm (b) Is the image for the object at distance 31.6 real or virtual? real virtual Is the image for the object at distance 15.8 real or virtual? real virtual Is the image for the object at distance 7.9 real or virtual? real virtual (c) Is the image for the object at distance 31.6 upright or inverted? upright inverted Is the image for the object at distance 15.8 upright or inverted? upright inverted Is the image for the object at distance 7.9 upright or inverted? upright inverted (d) Find the magnification for the object at distance 31.6 cm Find the magnification for the object at distance 15.8 cm Find the magnification for the object at distance 7.9 cm

Explanation / Answer

For do = 31.6 cm:

1/31.6 + 1/di = 1/(-15.8)

=> di = -15.8 * 31.6 / (15.8 + 31.6) = -10.5 cm

Negative sign of image distance means image is virtual and formed on the same side of the lens as the object.

magnification, m = -di / do = -(-10.5) / 31.6 = 0.33

Positive sign of magnification means image is upright.

For do = 15.8 cm:

1/15.8 + 1/di = 1/(-15.8)

=> di = -15.8 * 15.8 / (15.8 + 15.8) = -7.9 cm

Negative sign of image distance means image is virtual and formed on the same side of the lens as the object.

magnification, m = -di / do = -(-7.9) / 15.8 = 0.5

Positive sign of magnification means image is upright.

For do = 7.9 cm:

1/7.9 + 1/di = 1/(-15.8)

=> di = -15.8 * 7.9 / (15.8 + 7.9) = -5.3 cm

Negative sign of image distance means image is virtual and formed on the same side of the lens as the object.

magnification, m = -di / do = -(-5.3) / 7.9 = 0.67

Positive sign of magnification means image is upright.

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