A 10 cm tall card with some cut-outs is placed on a long table in front of a lamp in a dark room as shown in the figure. The lamp is 15 cm tall and is placed 15 cm in front of the card. Which of the options shows the correct shadow cast by the card?
To determine the correct shadow cast by the card when illuminated by a lamp, we analyze the setup geometrically. The card is placed 15 cm away from a 15 cm tall lamp in a dark room. This creates a scenario where the card, including its cut-outs, will cast a shadow opposite to the light source on the table. Consider the following analysis:
The height of the lamp and its position relative to the card means that the top of the lamp will illuminate the area directly opposite and along a similar line of sight, forming a shadow in the line of the cut-outs.
The card is 10 cm tall, and since it is directly facing a 15 cm tall lamp, the shadow's height will correspond roughly to the lamp's positioning at this 15 cm distance.
The correct shadow should match the cut-out pattern of the card, accounting for vertical light source projection at this consistent height.
The correct shadow pattern should thus align with the lamp's height and positioning as depicted.
Upon examining the given options:
The shadow that accurately corresponds to the setup described is . This option reflects the accurate projection of the card's cut-outs as influenced by a 15 cm tall lamp placed 15 cm away in the given conditions.
