1. Bangalore’s latitude is roughly 13˚N. At noon, on one day during which months would
a vertical object cast no shadow?
a. June and Dec
b. Apr and Aug
c. Mar and September
d. May and November.

Correct option: (b) April and August

At Bengaluru’s latitude (about 13° N), a vertical object casts no shadow at local noon on two “zero shadow days” each year, when the Sun is exactly overhead and its rays fall vertically.​

Concept: Zero Shadow Day and Latitude

Zero shadow day (also called zenith Sun day) occurs when the Sun’s declination equals the observer’s latitude, so the Sun is at the zenith at noon and vertical objects have no horizontal shadow.​

The Sun’s declination varies between about 23.4° N (Tropic of Cancer) and 23.4° S (Tropic of Capricorn) during the year, so zero shadow days are possible only for places lying between these two tropics.​

Applying it to Bengaluru (13° N)

• Bengaluru’s latitude ≈ 13° N, which is between the Equator (0°) and Tropic of Cancer (23.4° N).​

• As the Sun’s declination moves northward from 0° to 23.4° N (around March–June) and then southward from 23.4° N back to 0° (around June–September), it equals 13° N twice.​

• These two crossings occur roughly in late April (northward journey) and mid–August (southward journey), giving Bengaluru two zero shadow days near these months.​

Hence, the month pair closest to these actual dates is April and August → option (b).

Why the Other Options Are Wrong

Option (a) June and December

• Around 21 June, the Sun is overhead at the Tropic of Cancer (23.4° N), not at 13° N, so it passes north of Bengaluru and cannot be exactly overhead there.​

• Around 22 December, the Sun is overhead at the Tropic of Capricorn (23.4° S), far south of Bengaluru, so a vertical object in Bengaluru will cast a definite shadow.​

So, June and December do not correspond to zero shadow days at 13° N.

Option (c) March and September

• Around the equinoxes in March and September, the Sun’s declination is about 0°, meaning it is overhead at the Equator, not at 13° N.​

• At 13° N during equinoxes, the Sun is to the south at noon, so a vertical object still has a noticeable shadow directed slightly to the north.​

Therefore, March and September are not zero shadow months for Bengaluru.

Option (d) May and November

• By May, the Sun’s declination has already passed 13° N and is closer to 20–23° N, so it is north of Bengaluru and not exactly overhead there.​

• In November, the Sun’s declination has moved south of the Equator (negative declination), closer to 10–20° S, again not matching 13° N.​

Thus, May and November cannot give noon zero shadow at 13° N.

Final Answer Recap

• Condition for no shadow at noon: Sun’s declination = latitude of the place.​

• For Bengaluru (13° N): This happens twice each year, approximately in late April and mid–August.​

• Correct option: (b) April and August.

SEO-Friendly Introduction

Zero shadow day in Bangalore at 13 degree north is a classic geography and astronomy concept frequently asked in competitive exams. It explains why, on two specific days each year around April and August, a vertical object in Bengaluru casts no shadow at noon when the Sun is exactly overhead.​